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A  LABORATORY  COURSE 
IN  PHYSICS 

FOR  SECONDARY  SCHOOLS 


BY 


EGBERT  ANDREWS  MILLIKAN,  PH.D. 

ASSISTANT  PROFESSOR  IN  PHYSICS  AT  THE  UNIVERSITY  OF  CHICAGO 


HENRY  GORDON  GALE,  PH.D. 

INSTRUCTOR  IN  PHYSICS  AT  THE  UNIVERSITY  OF  CHICAGO 


I  to 


f  GINN  &  COMPANY 

i^l 

\  '  BOSTON  •  NEW  YORK  •  CHICAGO  •  LONDON 

\ 

NOV 


COPYRIGHT,  1906,  BY 
ROBERT  A.  MILLIKAN  AND  HENRY  G.  GALE 


ALL  RIGHTS  RESERVED 
66.8 


gbe   fltfttnaum  j>rc« 

GINN   &  COMPANY  •   PRO- 
.  PRIETORS  •  BOSTON  •  U.S.A. 


ac-35 


INTRODUCTION 

Although  laboratory  work  is  now  generally  recognized  as  an 
indispensable  part  of  any  adequate  course  in  elementary  physics,' 
it  is  nevertheless  a  lamentable  fact  that  there  are  still  some 
schools  in  which  it  is  not  attempted  at  all,  while  there  are 
others  in  which,  despite  the  most  expensive  equipment,  the 
laboratory  fails,  on  the  whole,  either  to  interest  or  instruct. 

Both  of  these  conditions  are  probably  attributable  to  one  and 
the  same  cause.  In  our  modern  glorification  of  the  laboratory, 
method,  particularly  of  exact,  quantitative  measurements,  and  in 
our  haste  to  get  away  from  the  superficial,  descriptive  physics  of 
thirty  years  ago,  some  of  us  have  undoubtedly  gone  so  far  as  to 
defeat  our  own  aims.  We  have  made  the  laboratory  an  impos- 
sibility in  schools  which  are  financially  weak,  because  we  have 
made  its  expense  prohibitive ;  and  we  have  made  it  a  disap- 
pointment in  other  schools  which  are  financially  strong,  because 
in  our  eagerness  to  show  our  students  exactly  how  much  we 
have  neglected  to  show  them  how  and  why.  In  short,  the  gravest 
danger  which  threatens  the  efficiency  of  the  high-school  labora- 
tory to-day  is  the  danger  which  arises  from  the  creeping  over  of 
the  methods  and  the  instruments  of  research  and  specialization 
from  the  university  into  the  high  school,  where  they  have  abso- 
lutely no  place,  —  the  danger  that  principles  shall  be  lost  sight 
of  in  the  bewildering  details  of  refined  methods  and  refined 
instruments. 

The  primary  aims  of  the  authors  in  the  development  of  this 
course  have  been :  (1)  to  make  it  a  continuous  and  inspiring 
laboratory  study  of  physical  phenomena,  and  as  far  as  possible 


iv  INTRODUCTION 

removed  from  a  mere  drill  in  physical  manipulation ;  and  (2)  to 
reduce  apparatus  to  its  simplest  possible  terms  and  yet  to  present 
a  thorough  course  in  laboratory  physics. 

Such  success  as  has  been  attained  in  the  accomplishment  of 
these  ends  has  been  due  not  merely  to  a  large  amount  of  labor 
and  experimentation  on  the  part  of  the  authors,  but  also  to  sug- 
gestions which  have  come  in  from  the  score  of  schools  in  which 
this  course  has  been  given  a  thorough  trial  during  the  past  three 
years,  and  especially  to  the  expert  assistance  of  the  instrument 
maker,  Mr.  William  Gaertner,  who  has  so  simplified  the  design  of 
the  apparatus  herewith  presented  that  a  large  part  of  it  can  now 
be  made  at  home  if  desired.  Even  if  it  is  all  purchased,  it  need 
not  cost  more  than  fifty  dollars  for  a  complete  set,  and  six  such  sets 
have  been  used  most  satisfactorily  at  the  University  of  Chicago 
in  conducting  laboratory  sections  of  twenty  pupils.  The  authors 
recommend,  however,  that  wherever  conditions  will  permit,  all 
of  the  pupils  of  a  section  be  kept  working  upon  the  same  experi- 
ment at  the  same  time.  This  arrangement  requires  about  half 
as  many  sets  as  there  are  pupils.  With  instructions  as  complete 
as  those  here  given,  the  experience  of  a  number  of  schools  has 
shown  that  with  fifteen  sets  one  instructor  can  successfully  con- 
duct a  class  of  as  many  as  thirty  pupils.  Great  care  has  been 
taken  to  incorporate  only  such  experiments  as  experience  has 
shown  to  be  workable  with  large  classes  and  with  a  minimum 
tax  upon  the  teacher's  time  outside  of  laboratory  hours. 

Another  feature  of  the  course  is  that  the  experiments  do  not 
presuppose  either  any  previous  study  of  the  subject  involved, 
or  any  antecedent  knowledge  of  physics.  The  laboratory  work 
may  be  kept  in  advance  of  the  class-room  discussion  throughout 
the  entire  course  if  desired.  Indeed,  in  their  own  elementary 
work  the  authors  prefer  to  let  more  than  half  of  the  experiments 
constitute  the  student's  first  introduction  to  the  subject  treated. 
Furthermore,  students  are  neither  instructed  nor  advised  to  study 


INTRODUCTION  v 

their  experiments  before  entering  the  laboratory,  for  each  experi- 
ment has  been  arranged  to  carry  with  it  its  own  introduction. 

As  was  to  have  been  expected  from  the  statement  of  the  aims 
of  the  course,  it  has  been  made  a  thorough  mixture  of  qualitative 
and  quantitative  work.  Indeed,  the  endeavor  to  make  an  ele- 
mentary laboratory  course  either  wholly  qualitative  or  wholly 
quantitative  seems  to  the  authors  to  result  inevitably  in  artifi- 
cial and  irrational  distinctions,  and  to  be  perhaps  the  most 
fruitful  cause  of  the  failure  of  laboratory  work. 

The  most  approved  and  most  satisfactory  division  of  time 
between  the  class  room  and  the  laboratory  is  three  single  periods 
per  week  in  the  former  and  two  double  periods  in  the  latter. 
Abundant  experience  in  schools  quite  variously  situated  has 
shown  that  the  work  herein  outlined  can  be  easily  completed  in 
two  such  eighty-  or  ninety-minute  periods  per  week  for  thirty- 
six  weeks,  even  when  all  the  notebook  work  is  done  in  class. 
The  length  of  the  experiments  has  not,  however,  been  adjusted 
so  as  to  fit,  in  all  cases,  one  school  period ;  first,  because  the 
lengths  of  school  periods  are  so  different  in  different  schools, 
and  second,  because  the  authors  have  not  wished  to  sacrifice  the 
logical  development  of  a  subject  to  a  consideration  which  is 
after  all  wholly  artificial  and  mechanical.  The  division  into  ex- 
periments is  made  on  the  basis  of  subject-matter  rather  than  of 
time.  A  considerable  number  of  the  experiments  will  be  found 
to  require  two  periods,  while  in  a  few  instances  two  experiments 
can  be  performed  in  a  single  period.  This  arrangement  has  not 
been  found  to  be  at  all  objectionable  where  all  of  the  pupils 
work  simultaneously  upon  the  same  experiment,  and  even  in 
courses  which  are  conducted  with  but  a  few  sets  of  apparatus 
the  difficulties  arising  from  this  source  have  been  found  to  be 
trifling. 

In  case  individual  teachers  find  it  desirable  to  shorten  or 
modify  the  course,  the  subdivisions  of  each  experiment  make 


vi  INTRODUCTION 

omissions  easy  and  simple.  It  has  been  an  especial  aim  of  the 
authors  to  make  both  this  course  and  the  class-room  text  which 
it  is  designed  to  accompany  sufficiently  flexible  to  give  full 
play  to  the  individuality  of  the  teacher.  Both  books  have  there- 
fore been  made  complete  enough  to  allow  of  a  considerable  range 
of  choice.  The  two  books  together  constitute  a  one-year  course 
in  high-school  physics.  The  laboratory  portion  has,  however, 
been  made  completely  independent  of  the  other  portion,  and  in 
a  number  of  instances  has  been  given  as  a  short  course  by 
itself  with  very  satisfactory  results.  It  is  the  firm  conviction 
of  the  authors,  based  upon  a  considerable  experience,  that  in 
schools  in  which  only  a  short  course  in  physics  can  be  offered, 
a  course  of  this  sort  with  laboratory  work  for  its  backbone  is 
much  more  satisfactory  than  one  based  upon  an  abridgment  of 
a  class-room  text. 

With  respect  to  the  notebook  the  authors  can  express  but 
little  sympathy  with  any  rigid,  mechanical  form  of  arrangement 
to  which  all  experiments  must  be  forced  to  conform,  and  they 
are  convinced  that  in  some  schools  the  real  study  of  physics  has 
been  sacrificed  to  the  study  of  notebook  form.  Their  directions 
to  their  own  pupils  are,  "Fill  out  your  notebook  as  you  proceed 
with  your  work  in  the  laboratory,  and  let  it  be  merely  a  brief 
running  record  of  what  you  do,  of  what  results  you  obtain,  and 
of  what  conclusions  you  draw."  Blank  books  of  coordinate 
paper  are  required,  and  left-hand  pages  are  used  for  scratch- 
book  purposes,  i.e.  they  contain  preliminary  observations  and 
computations,  while  right-hand  pages  contain  the  orderly  out- 
line of  the  work,  including  the  title  and  subheads  of  each 
experiment  as  found  in  the  manual,  a  very  brief  statement 
of  what  is  done  under  each,  an  orderly  statement  of  results 
(copied  in  some  instances  from  the  left-hand  page),  and  conclu- 
sions. Outline  drawings  are  encouraged  whenever  the  idea  can 
be  expressed  more  quickly  and  clearly  in  a  drawing  than  in 


INTKODUCTION  vii 

words.  In  order  to  place  especial  insistence  upon  the  conclu- 
sions, questions  have  been  freely  scattered  through  the  text, 
the  answers  to  which  generally  involve  the  conclusions  which 
are  to  be  drawn.  In  schools  in  which  double  laboratory  periods 
cannot  be  obtained  time  may  be  gained,  without  sacrificing 
the  real  study  of  physics,  by  having  the  orderly  part  of  the 
notebook  work  done  at  home.  If  still  further  time  must  be 
gained,  the  authors  prefer  to  save  it  at  the  expense  of  the  writ- 
ten work  rather  than  at  that  of  the  experiments,  oral  answers 
and  discussion  in  the  laboratory  replacing  some  of  the  written 
work  called  for. 

For  the  benefit  of  those  who  use  both  this  book  and  the 
authors'  class-room  text  a  suggested  time  schedule  for  a  thirty- 
six  weeks'  school  year  is  inserted  in  Appendix  A.  Whether 
this  particular  schedule  is  followed  or  not,  it  seems  to  the 
authors  a  matter  of  great  importance  that  each  teacher  begin 
his  year  with  some  well-considered  time  schedule  before  him, 
and  that  he  plan  each  lesson  and  make  his  omissions  and  addi- 
tions with  this  schedule  in  mind.  Otherwise  it  almost  invariably 
happens  that  the  subjects  treated  in  the  first  half  of  the  text 
receive  a  disproportionate  amount  of  time. 

In  Appendix  C  will  be  found  a  complete  list  of  the  apparatus 
desirable  for  the  course.  The  experiments  do  not,  however, 
preclude  the  use  of  the  more  expensive  forms  of  instruments 
which  are  already  common  in  the  equipment  of  high  schools, 
although  the  authors  believe  the  simpler  apparatus  to  be,  in 
general,  the  more  instructive. 

The  form  which  has  been  given  to  the  Boyle's  Law  experi- 
ment (page  26)  was  first  called  to  the  authors'  attention  by  Mr. 
C.  H.  Perrine  of  the  Wendell  Phillips  High  School,  Chicago, 
although  a  modification  of  the  same  method  is  found  in  the 
admirable  laboratory  manual  by  Nichols,  Smith,  and  Turton." 
The  experiment  on  the  cooling  of  acetamide  through  its  change 


viii  INTRODUCTION 

of  state  is  the  authors'  modification  of  a  similar  experiment  on 
acetanilid  suggested  to  them  by  Dr.  C.  E.  Linebarger  of  the 
Lake  View  High  School,  Chicago.  The  experiment  on  the 
mechanical  equivalent  of  heat  (Experiment  20)  is  similar  to  one 
described  in  Edser's  Heat.  The  remaining  experiments  are  either 
so  familiar  as  to  be  common  property  or  else  have  been  devised 
by  the  authors.  The  single  balance,  which  serves  all  the  pur- 
poses of  the  course,  was  designed  especially  for  it  by  Mr.  Gaert- 
ner,  with  a  view  to  gaining  the  great  advantages  which  the 
suspended-beam  type  of  balance  possesses  over  the  trip  scale, 
and  at  the  same  time  doing  away  with  the  nuisance  of  small 
weights.  The  apparatus  used  in  the  study  of  electricity  is  nearly 
all  new,  and,  though  very  inexpensive  and  apparently  crude,  has 
proved  extremely  satisfactory.1 

Among  the  large  number  of  teachers  who  have  already  used 
the  course  and  who  have  assisted  in  perfecting  it,  the  authors 
are  under  especial  obligation  to  Dr.  G.  M.  Hobbs,  Dr.  C.  J. 
Lynde,  and  Mr.  F.  H.  Wescott  of  the  University  High  School, 
Mr.  George  Winchester,  now  of  Washington  State  University, 
and  Mr.  Harry  D.  Abells  of  Morgan  Park  Academy. 

R.  A.  M. 
II.  G.  G. 

1  All  of  the  apparatus  for  the  course  can  be  obtained  of  William  Gaertner  & 
Co.,  5347  Lake  Avenue,  Chicago. 


CONTENTS 


EXPERIMENT  PAGE 

1.  DETERMINATION  OF  TT * 1 

2.  VOLUME  OF  A  CYLINDER 3 

3.  DENSITY  OF  STEEL  SPHERES 8 

4.  RESULTANT  OF  Two  FORCES 11 

5.  PRESSURE  WITHIN  A  LIQUID 14 

6.  USE  OF  MANOMETERS 17 

7.  ARCHIMEDES'  PRINCIPLE 19 

8.  DENSITY  OF  LIQUIDS 21 

9.  DENSITY  OF  A  LIGHT  SOLID 24 

10.  BOYLE'S  LAW 20 

11.  DEW-POINT 30 

12.  HOOKE'S  LAW .35 

13.  EXPANSION  OF  AIR         .         .         .         .         .         .         .         .         .         .37 

14.  EXPANSION  OF  BRASS 40 

15.  PRINCIPLE  OF  MOMENTS 44 

1C.  THE  INCLINED  PLANE 46 

17.  THE  PEN-DILI  M 48 

18.  THE  LAW  OF  MIXTURES 52 

19.  SPECIFIC  HEAT 55 

20.  THE  MECHANICAL  EQUIVALENT  OF  HEAT  .         ,         .         .         .59 

21.  COOLING  THROUGH  CHANGE  OF  STATE 62 

22.  HEAT  OF  FUSION  OF  ICE 64 

23.  BOILING  POINT  OF  ALCOHOL 66 

24.  FREEZING  AND  BOILING  POINTS  OF  WATER 68 

25.  MAGNETIC  FIELDS  .         .         .  .         .         .  .         .70 

26.  MOLECULAR  NAT*URE  OF  MAGNETISM  .         .  .         .         .         71 

27.  STATIC  ELECTRICAL  EFFECTS 74 

ix 


X  CONTENTS 

EXPERIMENT  PAGE 

28.  THE  VOLTAIC  CELL 79 

29.  MAGNETIC  EFFECT  OF  A  CURRENT       * 82 

—         • 

30.  MAGNETIC  PROPERTIES  OF  COILS 85 

31.  ELECTROMOTIVE  FORCES 87 

32.  OHM'S  LAW 91 

33.  COMPARISON  OF  RESISTANCES 93 

34.  INTERNAL  RESISTANCE 97 

35.  ELECTROLYSIS  AND  THE  STORAGE  BATTERY 99 

36.  INDUCED  CURRENTS 102 

37.  ELECTRIC  BELLS  AND  MOTORS 106 

38.  SPEED  OF  SOUND  IN  AIR 107 

39.  VIBRATION  RATE  OF  A  FORK  .         .         .         .         .         .         .         .  108 

40.  WAVE  LENGTH  OF  A  FORK ,  .         .110 

41.  LAWS  OF  VIBRATING  STRINGS Ill 

42.  PLANE  MIRRORS 113 

43.  INDEX  OF  REFRACTION 114 

44.  CRITICAL  ANGLE  OF  GLASS 116 

45.  CONCAVE  MIRRORS 118 

46.  CONVEX  LENSES 119 

47.  MAGNIFYING  POWER  OF  A  SIMPLE  LENS 121 

48.  THE  ASTRONOMICAL  TELESCOPE 122 

49.  THE  COMPOUND  MICROSCOPE 123 

60.  PRISMS 124 

61.  PHOTOMETRY 128 

APPENDIX  A 129 

APPENDIX  B 130  ' 

APPENDIX  C 131* 

INDEX   .  .  133 


LABORATORY  PHYSICS 
/*.*/* 

EXPERIMENT  1 
EXPERIMENTAL   DETERMINATION   OF   TT 

(The  ratio  of  the  circumference  of  a  circle  to  its  diameter) 

(a)  Measurement  of  circumference.  Measure  the  circumference 
to  an  accurately  turned  disk  in  the  following  way.  Scratch  a 
short  mark  A  (Fig.  1)  on  the 
face  of  the  disk  perpendicu-  M(  O 
lar  to  its  edge.  Stand  the  disk 
on  edge  on  a  meter  stick  so  B  FIG  ^ 

that  the  mark  A  is  very  accu- 
rately above  some  chosen  division  B,  e.g.  the  10-cm.  mark  of  the 
meter  stick. 

Then,  supporting  the  disk  by  causing  the  thumb  and  fore- 
finger  to  meet  through  0,  roll  it  very  carefully  along  the 
meter  stick  until  it  has  turned  through  one  complete  revolu- 
tion.  (Don't  touch  circumference  in  rolling.)  The  mark  A  will 
fall  on  some  point  of  the  scale.  If  it  does  not  fall  exactly  on 
one  of  the  millimeter  divisions,  in  order  to  retain  a  decimal 
system  throughout,  record  the  fractional  part  of  the  last  divi- 
sion in  tenths,  not  in  halves,  thirds,  or  quarters.1 

1  Unfamiliarity  with  the  metric  system  may  make  it  seem  more  natural  to 
estimate  in  halves,  thirds,  or  quarters,  but  it  will  be  easy  to  express  the  result 
in  tenths  if  one  reflects  that  .4  is  a  little  less,  and  .6  a  little  more,  than  1/2;' 
.2  a  little  less  and  .3  a  little  more  than  1/4;  .1  a  little  less  than  .2,  i.e. 

1/5,  etc. 

1 


2  LABORATORY  PHYSICS 

Repeat  the  measurement  and  estimation  four  times,  starting 
at  a  different  point  on  the  scale  each  time.  Take  a  mean  of 
these  five  readings  as  the  most  correct  value  of  the  circumfer- 
ence obtainable  by  this  method. 

Since  the  separate  observations  were  uncertain  in  the  tenths 
millimeter  place,  the  mean  will  surely  be  uncertain  in  the 
hundredths  millimeter  place.  To  reserve  places  beyond  this, 
then,  would  not  only  be  useless  but  misleading,  since  it  would 
indicate  that  the  measurement  was  made  to  a  higher  degree 
of  accuracy  than  it  really  was.  The  best  usage  in  recording 
physical  observations  is  to  record  one  uncertain  figure,  but 
never  more,  except  in  recording  the  mean  of  a  considerable 
number  of  observations,  when  one  more  figure  may  be  retained, 
especially  if  the  difference  between  the  individual  observations 
is  slight.  If  this  uncertain  figure  hap- 

ii. , , . i .^.^.,1,^^^^     pens  to  be  zero,  it  should  be  recorded 
like  any  other  digit. 

(b)  Measurement   of  diameter.    Next 

measure  the  diameter  of  the  ring  with  a  meter  stick  held  on 
edge  as  in  Fig.  2.  Record  five  observations  taken  along  differ- 
ent diameters,  and  take  the  mean,  estimating  in  each  case  to 
tenths  of  a  millimeter. 

(c)  Computation.  From  these  measurements  compute  TT,  the 
ratio  of  the  circumference  of  a  circle  to  its  diameter.  In  the 
result  save  only  one  uncertain  figure. 

To  find  the  first  uncertain  figure  in  the  result,  divide  as  in 
8.436 126.52  |3.143     the  illustration,  underlining  the  uncertain 
~~25308~  figures  throughout. 

1  2120  Compare  the  result  of  your  measurement 

8436  with  that  given  by  mathematical  theory, 

36840  viz.  3.1416.    Find  first  the  amount  of  the 

33744  error,   and   then   compute  what  per  cent 

30960  the  error  is  of  the  whole  quantity,  e.g.  if 


VOLUME  OF  A  CYLINDER  3 

the  result  of  your  measurement  is  3.143,  then  by  taking  the 
difference  between  this  and  3.1416  we  get 

3.143  1%  of  3.1416  =  .031416 

3.1416  .0014 

.-.  Per  cent  of  error  =  =  .045 

.0014  =  error  .031 

In  the  last  division  only  two  significant  figures  were  used  in  the 
denominator,  since  it  is  never  necessary  to  find  the  per  cent  of 
error  to  more  than  this  degree  of  accuracy. 

Record  measurements  and  computations  as  below : 

Trial  Diameter  Circumference 

1  8.43  26.50 

2  8.45  26.55 

3  8.44  26.52  Circumference 

4  8.43  26.50  Diameter 

5  8.43  26.52  Error  =  .0014 

Mean  8.436  26.51.8  Per  cent  of  error  =  .045 

State  in  the  notebook,  beneath  the  results  tabulated  as  above, 
what  per  cent  of  error  would  have  been  introduced  into  the  result 
if  you  had  made  an  error  of  .1  mm.  in  measuring  the  diameter. 
(Find  what  per  cent  .1  mm.  is  of  the  whole  diameter  8.436.) 

State,  therefore,  whether  your  error  is  more  or  less  than 
should  have"  been  expected  from  reasonably  careful  measure- 
ments. (Put  your  answers  into  the  form  of  complete  sentences.) 

EXPERIMENT  2 
DETERMINATION  OF  THE  VOLUME  OF   A  CYLINDER 

I.  By  computation  from  linear  measurement. 

(a)  Measurements.  Measure  with  a  metric  rule  the  inside 
depth  of  the  cylindrical  vessel  shown  in  Fig.  8,  in  three  differ- 
ent places,  estimating  as  before  very  carefully  to  tenths  of  a 
millimeter. 


LABORATORY  PHYSICS 


Measure  the  inside  diameter  D  with  a  vernier  caliper,1  if  this 
instrument  is  available;  if  not,  use  the  method  of  the  previous 
experiment,  taking  pains  that  the  edge  of  the  meter  stick  is  held 
in  every  case  exactly  across  a  diameter. 

(b)  Computation.    Compute  the  volume  of  the  cylinder  from 

the  area  of  the  base  (-^r->  or  TUP,  K  being  the  radius  j  and  the 

height  L.    Underline  all  uncertain  figures,  and  save  only  two 
uncertain  figures  in  the  result. 

The  following  illustrates  the  method  of  computation  : 


L=    8.01 


fi  =  2.513  cm. 
2.513 

AJ2  =  6.315 
TT  =  3.142 

7539 
2513 
12565 
5026 

12630 
25250 
6315 
18945 

6.315 

7T.K2  =  19.841 

1984 
15872 
158.91 


=  volume 

in  cubic 

centimeters 


1  The  vernier  is  a  device  for  measuring  fractional  parts  of  a  scale  division.  It 
consists  of  a  movable  scale  AB  arranged  to  slide  along  a  fixed  scale  CD  (Fig.  3). 
e  f      The  object  to  be  measured  is  placed  between  the  jaws  EF, 

which  are  so  made  that  when  they  are  in  contact  the  zero 
of  the  sliding  scale  is  opposite  the  zero  of  the  fixed  scale. 


FIG.  3 

Ten  divisions  of  the  sliding  scale  A E  are  made  equal  to 
nine  divisions,  i.e.  9  mm.,  on  the  main  scale  CD;  hence 
one  vernier  division  is  equal  to  .9  mm.  Fig.  4  (1)  shows 
the  vernier  scale  and  the  fixed  scale  enlarged.  Here 
the  zero  of  the  vernier  is  exactly  opposite  the  5-mm. 
mark  of  the  fixed  scale,  this  being  the  relative  position  of  the  two  scales  when 
an  object  6  mm.  in  diameter  is  placed  between  the  jaws.  Since  one  division  on 


VOLUME  OF  A  CYLINDER  5 

Tabulate  your  results  in  some  form  similar  to  the  following : 

First  Second  Third 

observation      observation  observation 

Height  of  cylinder  =  8.26  cm.       8.25  cm.  8.25  cm.     8.253  cm. 

Inner  diameter  of  cylinder  =  6.04  cm.       6.03  cm.  6.04  cm.     6.03J7  cm. 

.• .  R  =  3 .019  .-.  Volume  =  236.2  cc. 

Write  in  your  notebook  answers  to  the  following  questions, 
using  complete  sentences  as  in  Experiment  1. 

If  the  diameter  of  a  circle  is  measured  as  10.1  cm.  when  it  is 
actually  10  cm.,  by  what  per  cent  will  the  square  of  the  diameter 
as  measured  differ  from  the  square  of  the  true  diameter?  (If  in 
doubt,  work  it  out.)  Hence  what  per  cent  of  error  will  be  intro- 
duced into  the  computed  value  of  the  area  of  a  circle,  if  there  is 
an  error  of  0.3  per  cent  in  the  measurement  of  the  diameter? 

AB  is  equal  to  only  .9  mm.,  while  one  division  on  CD  is  equal  to  a  whole  milli- 
meter, it  follows  that  the  mark  1  of  the  sliding  scale  AB  is  .1  mm.  behind  the 
mark  6  of  the  fixed  scale;  2  on  AB  is  .2  mm.  behind  7  on  CD;  3  is  .3  mm. 
behind  8 ;  7  is  .7  mm.  behind  12,  etc.  Therefore,  if  the  sliding  scale  were  moved 
up  so  as  to  bring  its  mark  1  opposite  the  mark  6  on  the  fixed  scale,  its  zero  mark 
would  move  up  .1  mm.  beyond  5.  If  the  vernier  had  moved  up  until  its  5  mark 
were  opposite  10  on  CD,  the  zero  mark  would  have  moved  .5  mm.  beyond  5,  etc. 
In  general,  then,  it  is  only  necessary  to  observe  which  mark  on  the  sliding  scale 

(1)  (2) 

Co    I     i    3    »     5    6     7    8    9     10   II    It    !3    l«    .5  It  17  D  C  0     I     8  .  J     »     5     «     >     •     »     '0    n     *  .13  D 


1 1 1 1 1     1 1 1 1 1       III          I  1 1  ^\}\\\ 

FIG.  4 

AB  is  directly  opposite  a  mark  on  CD,  in  order  to  know  how  many  tenths  of  a 
millimeter  the  zero  mark  of  AB  has  moved  beyond  the  last  division  passed  on 
CD.  Thus  the  reading  in  Fig.  4  (2)  is  3.7  mm.  (.37  cm.),  since  the  zero  mark 
of  the  vernier  has  passed  the  3-mm.  mark  on  the  fixed  scale  CD,  and  the  7  mark 
on  the  vernier  is  directly  opposite  some  mark  of  CD. 

In  order  that  the  interior  as  well  as  exterior  dimensions  of  hollow  objects  may 
be  readily  determined,  the  jaws  ef  (Fig.  3)  are  added  in  many  vernier  calipers. 
These  jaws  are  inserted  just  inside  the  walls  and  the  reading  taken  as  described. 


LABORATORY  PHYSICS 


If  you  misread  the  diameter  of  your  cylinder  by  0.1  mm.,  what 
per  cent  of  error  did  you  thus  introduce  into  the  diameter? 
into  the  computed  area  of  the  base  of  the  cylinder?  into  the 
computed  volume  of  the  cylinder? 

II.  By  weighing  the  cylinder  first  when  empty  and  then  when 
filled  with  water. 

(a)  Weighing  cylinder  by  method  of  substitution.  Place  the 
empty  cylinder  with  its  ground-glass  cover  on  the  pan  11  (Fig.  5) 
of  the  balance,  and  add  to  the  other  pan  any  convenient  objects, 
such  as  pieces  of  iron,  shot,  and  bits  of  paper,  until  the  pointer 
stands  opposite  the  middle  mark  at 
«,  the  rider  R  being  at  zero. 

Then  replace  the  cylinder  and 
cover  by  weights  from  the  set  in  the 
following  way.  Find  by  trial  the 
largest  weight  which  is  not  too 
large,  and  place  it  on  pan  B.  Add 
the  equal  weight,  or,  if  there  is  no 
equal,  the  next  smaller  one,  if  it  is 
not  too  heavy;  add  again  the  equal 
or  next  smaller  weight,  and  so  on, 
always  working  down  from  weights  which  are  too  large.  This 
saves  the  delay  and  annoyance  caused  by  adding  a  large  number 
of  small  weights  and  at  last  rinding  that  their  sum  is  still  too 
small. 

When  a  balance  has  been  obtained  to  within  10  g.,  slide 
the  rider  R  along  the  graduated  beam  until  the  pointer  stands 
opposite  the  middle  mark  at  s.  The  weight  of  the  body  is  then 
the  sum  of  the  weights  on  the  pan  plus  the  reading  of  the  left 
edge  of  the  index  R  on  the  graduated  beam.  Since  each  division 
of  the  scale  on  the  beam  represents  one  tenth  of  a  gram,  by 
estimating  to  fractional  parts  of  a  division  we  can  obtain  the 
weight  by  this  method  to  hundredths  of  a  gram. 


FIG.  5 


VOLUME  OF  A  CYLINDER  7 

The  preceding  is  the  rigorously  correct  method  of  making  a 
weighing.  It  is  called  the  method  of  substitution. 

(b)  Weighing  cylinder  by  usual  method.  Next  weigh  the  same 
object  by  the  following  simpler  and  quicker  method.  Empty  the 
pans,  move  R  to  its  zero  point,  and  bring  the  pointer  to  the 
middle  mark  by  altering  if  necessary  the  nut  n  (Fig.  5).  Then 
place  the  object  on  pan  A  and  find  what  weights  must  be  added 
to  pan  B  in  order  to  bring  the  pointer  to  the  middle  mark  again, 
the  adjustment  for  weights  smaller  than  10  g.  being  made 
as  above  with  the  rider.  Unless  the  difference  in  the  two  weigh- 
ings is  larger  than  one  or  two  tenths  of  a  gram,  you  may  hence- 
forth use  the  second  method  for  all  ordinary  weighings ;  for 
the  imperfections  in  inexpensive  commercial  weights,  such  as 
we  are  using,  are  likely  to  amount  to  as  much  as  a  tenth  of  a 
gram.  Hence  we  are  taking  needless  pains  and  adding  nothing 
to  the  accuracy  of  the  result  by  using  the  rigorous  method.1 

(<?)  Weighing  cylinder  full  of  water.  Ne^t  fill  the  cylinder  with 
water  and  place  the  cover  over  it,  taking  care  that  no  air  bubbles 
are  left  inside.  Carefully  wipe  all  moisture  from  the  outside 
and  weigh. 

Refill  the  cylinder  and  repeat  this  last  weighing  in  order  to 
see  how  closely  two  observations  can  be  made  to  agree.  From 
the  mean  of  these  two  weighings  and  the  mean  of  the  weigh- 
ings of  the  empty  cylinder  and  cover  find  the  weight  of  the 
water. 

Since  1  cc.  of  water  weighs  1  g.,  the  volume  of  the  cylinder 
in  centimeters  is  equal  to  the  weight  in  grams  of  the  water 
which  it  contains. 

1  The  new  method  would  be  as  correct  as  the  method  of  substitution,  provided 
we  could  know  that  the  two  balance  arms  are  of  exactly  the  same  length  (see 
Principle  of  Moments,  p.  44).  If,  therefore,  you  get  different  results  by  this 
method  and  the  method  of  substitution,  you  may  know  that  the  instrument 
maker  did  not  succeed  in  getting  the  balance  arms  quite  equal  in  length.  Errors 
due  to  this  cause  are,  however,  usually  very  slight. 


8  LABORATORY  PHYSICS 

Tabulate  results  as  follows : 

First  Second 

.  ,.  .  ,.  Mean 

weighing        weighing 

Weight  of  empty  cylinder  and  cover  =  221.6  g.      221.7  g.        221.65  g. 
Weight  of  cylinder  plus  water  =  456.8  g.       456.6  g.        456.7    g. 

.-.  Weight  of  water  alone  =  235.0  g.     .-.  Volume  =  235.0    cc. 

Difference  between  volume  by  I  and  II  =  236.2  -  235.0  =  1.2  g. 
Per  cent  of  difference  =  (1.2  *  235)  x  100  =  .51 

What  per  cent  of  error  would  an  error  of  .2  g.  in  the  weigh- 
ing of  the  cylinder  full  of  water  introduce  into  your  last  measure- 
ment of  the  volume  ? 

Do  your  results  in  I  and  II  agree  as  well  as  they  should 
in  view  of  the  probable  errors  which  you  have  estimated  are 
inherent  in  your  two  measurements  of  the  volume? 

Decide  from  your  results  which  method  of  finding  the  volume 
is  probably  the  more  accurate. 


EXPERIMENT  3 
DETERMINATION  OF  THE  DENSITY  OF  STEEL  SPHERES 

I.  From  weights  and  diameters  of  spheres. 
(a)  Diameters  of  spheres.    Measure  the  diameters  of  several 
steel  spheres  with  the  micrometer  caliper,1  if  this  instrument  is 

available.    If  not,  the  diameters 
may  be  obtained  by  placing  the 
balls  between  two  blocks,  as  in- 
Fir  6  dicated  in  Fig.  6,  and  measur- 

ing the  distance  between  the 
blocks.    If  this  method  is  used,  however,  it  will  be  better  to  place 

1  In  the  micrometer  caliper  (Fig.  7)  the  divisions  upon  the  scale  c  correspond 
to  the  distance  between  the  threads  of  the  screw  s.  This  distance  is  usually  a 
half  millimeter.  Hence  turning  the  milled  head  h  through  one  complete  revo- 
lution changes  the  distance  between  the  jaws  ab  by  exactly  one  half  millimeter, 


DENSITY  OF  STEEL   SPHERES 


9 


six  or  eight  balls  in  a  row  between  two  meter  sticks,  set  the 
blocks  at  the  ends  of  the  row,  and  divide  the  distance  between 
the  blocks  by  the  number  of  balls.  It  will  be  best  to  use  balls 
about  2  cm.  in  diameter.  Take  the  mean  of  at  least  five  diameter 
measurements. 

Compute  the  volume  of  a  sphere  from  the  relation  V=  |7rZ>3, 
where  V  represents  the  volume  and  I)  the  diameter.  Here,  and 
henceforth,  instead  of  underscoring  all  uncertain  figures  as 
heretofore,  you  may  simply  retain  in  any  product  or  quotient 
the  same  number  of  significant  figures  as  there  are  figures  in 
the  least  accurate  factor  which  enters  into  the  product  or  quo- 
tient. 

and  turning  h  through  one  fiftieth  of  a  revolution  changes  the  distance  between 
aJI)  by  -^  x  \  —  .01  mm.  If,  then,  there  are  fifty  divisions  upon  the  circumference 
of  d,  each  division  represents  a  motion  of  .01  mm.  at  b. 

To  make  a  measurement,  turn  up  the  milled  head  h  (Fig.  7)  until  the  jaws  ab 
are  in  contact,  i.e.  until  the  milled  head,  held  with  light  pressure  between  the 
thumb  and  finger,  will  slip  between  the  fingers  instead  of  rotating  further. 


FIG.  7 


Never  crowd  the  threads.  The  zero  of  the  graduated  circle  should  now  coincide 
with  the  line  ec  on  the  scale.  If  this  is  not  the  case,  have  the  instructor  adjust 
the  stop  a. 

Insert  the  object  to  be  measured  between  the  jaws  ab  and  again  turn  up  the 
milled  head  until  it  slips  between  the  fingers  when  held  with  the  same  pressure 
as  that  used  to  test  the  zero  reading.  Read  the  whole  number  of  millimeters 
and  half  millimeters  of  separation  of  the  jaws  upon  the  scale  ec  and  add  the  num-* 
ber  of  hundredths  millimeters  registered  upon  d.  This  is  the  thickness  of  the 
object. 


10  LABORATORY  PHYSICS 

The  following  illustrates  the  method  of  computation : 

D  =  2.534  cm.              IP  =  6.421  D3  =  16.27 

2.534                     D  =  2.534  TT  =  3.142 

10136                           25  684  3  254 

7602                           19263  6508 

1  267  0                          3  210  5  1  62  7 

5  068                            12  842  48  81 


D2  =  6.421  Z>3=16.27  irD8=  51.12 

6|51.12 

8.520  cc.  =  i  Tr/)3  =  Volume 

(b)  Weight  of  balls.  Weigh  ten  or  twelve  balls  all  at  once  on 
the  balances.  From  the  total  weight,  the  number  of  balls,  and 
the  volume  of  a  single  ball  find  the  density  of  steel,  i.e.  the 
number  of  grams  in  1  cc.  Record  thus : 

First        Second         Third         Fourth         Fifth 
ball  ball  ball  ball  ball 

Diameters:     19.053      19.050       19.048       19.047       19.050       19.050mm. 
.-.  Volume  of  1  ball  =  3.6216  cc.          Weight  of  12  balls  =  341.0  g. 
.-.  Weight  of  1  ball  =  28.42  g.          .-.  Density  of  steel       =  7.846 

II.  From  weight  of  spheres  and  weight  of  water  which  they 
displace.  Fill  a  cylindrical  vessel,  holding  about  150  cc.,  with 
water  and  cover  with  a  ground-glass  plate  (Fig. 
8),  carefully  excluding  all  air  bubbles.  Dry 
the  outside  and  place  on  the  left  pan  of  the  bal- 
ance. Place  on  the  same  pan,  beside  the  vessel 
of  water,  the  same  number  of  balls  used  in  I, 
and  find  the  weight  of  the  whole  load. 

Remove  the  vessel  of  water,  lift  off  the  cover, 
and  drop  the  balls  into  the  water.  Replace  the 
cover,  dry  the  outside  of  the  cylinder,  replace  it  on  the  balance 
pan,  and  weigh  again.  From  the  two  weighings  find  the  weight 
of  the  water  displaced  by  the  balls.  Since  1  cc.  of  water  weighs 
1  g.,  this  last  weight  is,  of  course,  the  volume  in  cubic  centimeters 


RESULTANT  OF  TWO  FORCES 


11 


of  the  displaced  water,  and  this  is,  of  course,  the  same  as  the 
volume  of  the  balls.  Find  the  weight  of  the  balls  alone  and 
thence  compute  the  density  of  steel.  Find  the  per  cent  of  dif- 
ference between  this  value  and  that  obtained  in  I.  Record  thus : 

Weight  of  12  balls  plus  cylinder  full  of  water  =  668.4  g. 

Weight  of  12  balls  in  cylinder  full  of  water  =  625.0  g. 

Weight  of  water  displaced  by  balls  =    43.4  g. 

Weight  of  12  balls  alone  (from  I)  =  341.0  g. 

.-.  Density  of- steel  =      7.85 

Per  cent  of  difference  between  results  of  I  and  II     =        .2 

State  in  your  notebook  which  of  the  above  methods  of  finding 
the  density  of  steel  you  consider  the  more  accurate,  giving  the 
reason  for  your  opinion. 

EXPERIMENT  4 

RESULTANT  OF  TWO  FORCES 

I.  Parallel  forces.  Support  two  spring  balances  from  nails, 
pegs,  or  tripod  rods,  as  in  Fig.  9,  and  so  choose  the  distance 


FIG.  9 


between  the  supports  that  the  meter  stick  ab  is  supported  at, 
say,  the  10-cm.  and  90-cm.  divisions. 

Record  the  readings  of  the  balances  1  and  2  (see  figure). 


12 


LABOR ATOKY  PHYSICS 


Hang  from  the  50-cm.  mark  a  mass  JF  which  you  have  already 
weighed  on  one  of  the  spring  balances,  and  which  is  large 
enough  to  stretch  it  nearly  to  its  limit. 

Read  the  balances  1  and  2  and  call  the  differences  between 
these  readings  and  the  initial  readings  Fl  and  Z\  respectively. 

Then  move  W  successively  to  the  40-cm.,  the  30-cm.,  and 
the  20-cm.  marks,  and  repeat  the  readings  for  each  position. 

Let  Zj  and  /2  represent  in  each  case  the  distance  in  decimeters 
from  the  point  from  which  W  is  hung  to  1  and  2  respectively. 
Record  as  indicated  below : 


Reading  of  1 :  without  W ; 

at  30  cm. ;    at  20  cm. 

Reading  of  2  :  without  W—    — ; 

at  30  cm ;    at  20  cm. 


IF  at  50  cm. 


at  40  cm. 


Wat  50  cm. 


at  40  cm.  • 


/>', 


State  in  your  notebook  what  you  learn  from  your  results 
regarding,  first,  the  magnitude  of  the  resultant  of  two  parallel 
forces ;  and  second,  the  product  of  either  of  the  two  forces  by 
its  distance  from  the  resultant. 

II.  Concurrent  forces.  Fasten  three  spring  balances  to  a  small 
ring  a  by  cords  about  8  in.  long,  and  slip  the  rings  of  the  bal- 
ances over  wooden  pegs  or  nails  in  a  board  AB  about  3  ft. 
square  (Fig.  10).  Choose  such  holes  for  the  pegs  that  each 
balance  is  stretched  to  at  least  one  half  of  its  full  range. 


RESULTANT  OF  TWO  FORCES 


13 


FIG.  10 


Slip  a  page  of  your  notebook  beneath  the  central  ring,  fasten 
it  down  with  thumb  tacks  or  weights,  and  with  a  sharp-pointed 
pencil  make  a  dot  on  the  paper  just  at  the  center  of  the  ring. 
Displace  the  ring  and  see  that      A 
its  center  comes  back  exactly  to 
the  same  position  as  at  first.    If 
this   is  not  the   case,  the  cause 
probably  lies  in  the  friction  which 
exists  between  the  balances  and 
the  table  top,  a  difficulty  which 
may  be  remedied  by  raising  the 
rings  slightly  on  the  pegs. 

Make  a  dot  exactly  beneath 
each  string  and  as  far  from  a  as 
possible  ;  then  take  the  three 
balance  readings. 

Unhook  each  balance  from  its 
peg  and  note  the  reading  of  the  pointer  as  the  balance  lies  flat 
on  the  table.  If  this  reading  is  less  than  zero,  add  the  suitable 
correction  to  the  balance  reading  recorded  on  the  paper;  if  it 
is  more  than  zero,  subtract  the  appropriate  amount. 

Remove  the  paper  and  with  great  care  draw  a  fine  line  from 
the  central  point  through  each  of  the  three  outside  points.  The 
direction  of  each  line  will  represent  the  direction  of  the  corre- 
sponding force. 

Measure  off  a  distance  on  each  line  which  shall  be  propor- 
tional to  the  corresponding  force,  choosing  any  convenient 
scale;  e.g.  if  the  forces  are  700,  1000,  and  1200  g.,  they  may 
be  conveniently  represented  by  lines  7,  10,  and  12  cm.  long. 

With  any  two  of  these  lines  as  sides  complete  a  parallelogram, 
using  a  ruler  and  compasses  to  get  the  sides  exactly  parallel. 
Draw  the  diagonal  of  this  parallelogram  from  the  central  point 
a,  measure  its  length,  and  find  the  magnitude  of  the  force  which 


14  LABORATORY  PHYSICS 

it  represents.  Thus,  if  the  diagonal  has  a  length  of  134  mm.,  it 
would  represent  in  the  foregoing  illustration  a  force  of  1340  g. 
Compare  with  the  reading  of  the  third  balance.  Tabulate  thus  : 

Reading  of  balance  1  =  —  Correction     =  —  .-.  F^     =  — 

Reading  of  balance  2  =  —  Correction    = 

Reading  of  balance  3  =  —  Correction    =  — 

Length  of  line  1  =  —  of  line  2       =  - 

Length  of  diagonal     =  -  .-.  Resultant  =  —          %  error  =  — 

State   in  your  notebook  what  you  have  proved  to  be  true 
regarding  the  magnitude  and  direction  of  the  resultant  of  two 
forces  which  meet  at  an  angle. 


EXPERIMENT  5 

PRESSURE  BENEATH   THE  FREE   SURFACE   OF 
A   LIQUID 

I.  Verification  of  the  law  of  depths  and  densities. 

(a)  Measurements  in  water.  Immerse  the  manometer 
Mot  Fig.  11  to  the  greatest  depth  possible  in  the  long 
glass  vessel  V  filled  with  water.1  A  length  of  at  least 
1  m.  is  desirable  (see  tube  of  Experiment  40). 

Measure  the  distance  from  the  surface  of  the  water  to 
the  top  of  the  mercury  in  the  short  arm,  and  record  this 
distance  as  the  first  depth.  Measure  the  distance  be- 
tween the  two  levels  of  the  mercury  in  the  two  arms 
of  the  manometer,  and  record  this  difference  as  the  first 


FIG.  11 


pressure.    (It  is  often  convenient  to  express  pressures  in 
this  way,  in  millimeters  of  mercury  instead  of  in  grams.) 
Raise  the  manometer  about  5  cm.  and  make  similar  measure- 
ments.   Continue  in  this  way,  diminishing  the  depth  about  5  cm. 
at  a  time,  until  the  surface  is  reached. 

1  A  piece  of  glass  tubing  about  1  m.  long,  4  or  5  cm.  in  diameter,  and  closed 
at  the  bottom  with  a  rubber  stopper  answers  the  purpose  admirably. 


PEESSUBE  WITHIN  A  LIQUID  15 

(b)  Measurements  in  gasoline.    Fill  the  vessel  V  with  gasoline 
instead  of  water,  and  make  another  set  of  similar  observations. 
Tabulate  results  as  follows  : 

WATER 
Depth  Pressure 


Pressure 
cm.       mm.       

—  cm.       mm. 

cm.  —  mm. 

etc.  etc.  etc.  etc. 

II.  Graphical  representation  of  a  direct  proportion.  When  two 
quantities  are  related  in  the  way  in  which  the  pressure  P  and 
the  depth  D  are  seen  to  be  related  above,  i.e.  when  making  one 
quantity  two,  three,  or  four  times  as  great  makes  the  other  two, 
three,  or  four  times  as  great,  the  one  quantity  is  said  to  be  directly 
proportional  to  the  other,  or  to  vary  directly  with  the  other. 

It  will  be  seen,  from  the  third  and  sixth  columns  above,  that 
the  ratio  between  the  two  quantities  D  and  P,  which  are  related 
in  this  way,  is  always  constant.  Hence,  if  Pv  P2,  P3,  etc.,  repre- 
sent the  pressures  at  depths  Dv  Z>2,  Z>3,  etc.,  then 

I),      P,     D,      P.  D,      !)„      !>„ 

— -  =  — -  >  — *  =  - l '  etc.,     or     — -  =  —  =  — »  etc., 
D          P        7)          P  P          P          P 

^2         •*!      ^3         ^3  *1         ^2         ^3 

or,  more  simply,  —  =  constant. 

This  is  the  analytic  or  algebraic  way  of  expressing  the  fact  that 
D  and  P  are  directly  proportional  to  each  other. 

A  third  way  of  expressing  the  relationship  between  two  quan- 
tities one  of  which  depends  for  its  value  upon  the  value  of  the 
other,  is  to  plot  them  in  a  "  graph,"  or  curve.  To  find  the 
nature  of  the  curve  which  represents  the  direct  proportionality 
of  this  experiment,  proceed  as  follows : 

Draw  two  straight  lines  OX  and  OF  on  a  piece  of  squared  ' 
(coordinate)  paper  (Fig.  12).    Represent  pressures  by  distances 


16 


LABORATORY  PHYSICS 


130 

S  25 

2 

B 

|  20 

S 
=   15 

1,0 


above  OX,  and  depths  by  distances  to  the  right  of  OF;  e.g.  let 

one  space  above  OX  represent  a  pressure  of  1  mm.  of  mercury, 

Y  M  an(l  one  space  to  the 

right  of  OF  represent  a 
depth  of  2  cm.  below  the 
surface  of  the  liquid. 
Any  point  on  the  line 
AB  will  therefore  rep- 
resent a  pressure  of 
18.5  rnm.  of  mercury, 
since  it  is  18.5  spaces 
aboveOX;  and  any  point 
on  CD  will  represent  a 
depth  of  25  cm.,  since 
this  line  is  12.5  spaces 
to  the  right  of  0  Y.  The 
point  b  at  the  intersec- 
tion of  these  lines  there- 
fore represents  a  pressure 
of  18.5  mm.  and  a  depth  of  25  cm.  Similarly,  if  the  table  shows 
that  the  pressure  is  29.6  mm.  when  the  depth  is  40  cm.,  this 
fact  will  be  represented  by  the  point  Z,  which  is  29.6  spaces 
above  OX  and  20  spaces  to  the  right  of  OF,  since  we  have 
chosen  to  let  one  space  in  the  direction  OX  stand  for  2  cm. 

Find  in  this  way  the  point  corresponding  to  each  depth  and 
its  corresponding  pressure  for  the  measurements  taken  in  water. 
These  points  will  be  found  to  lie  almost  exactly  on  a  straight 
line  ON.  With  a  sharp  pencil  and  a  ruler  draw  through  0  the 
straight  line  which  passes  as  close  as  possible  to  all  of  the 
plotted  points. 

In  a  similar  way  plot  for  the  readings  in  gasoline,  using  the 
same  axes,  OX  and  OF,  and  the  same  "scale";  i.e.  let  one 
space  above  OX  represent  a  pressure  of  1  mm.  of  mercury,  and 


10        20  C    30        40        50 
Depths  in  centimeters 

FIG.  12 


60       70 


MEASUREMENT  OF  PRESSURE  17 

one  space  to  the  right  of  OY  represent  a  depth  of  2  cm.1 
These  points  will  be  found  to  lie  almost  exactly  on  the  straight 
line  ON. 

We  learn,  therefore,  that  the  geometrical  or  graphical  inter- 
pretation of  a  direct  proportionality  is  a  straight  line. 

Divide  the  pressure  Cg,  which  your  graph  shows  to  exist  at  a 
given  depth  in  gasoline,  by  the  pressure  Cb  at  the  same  depth 
in  water.  The  density  of  gasoline  is  about  .71.  What  do  you 
get  by  this  division? 

Summarize  in  the  notebook  the  results  of  the  experiment, 
stating  first  in  words  the  law  which  expresses  the  relation 
between  pressure  and  depth,  as  proved  in  the  experiment; 
stating,  second,  what  is  the  analytic  expression  of  this  law; 
and,  third,  what  is  its  graphical  expression. 

State  also  why  dividing  Cg  by  Cb  in  Fig.  12  gave  us  the 
density  of  gasoline. 

EXPERIMENT  6 
MEASUREMENT  OF  PRESSURES  BY  MANOMETERS 

I.  Determination  of  the  densities  of  the  liquids  used  in  the 
manometers.  Weigh  a  glass-stoppered  bottle  having  a  capacity 
of  at  least  200  cc.,  first  when  empty,  then  when  filled  with 
water,  and  again  when  filled  with  gasoline.  Subtract  the  weight 
of  the  empty  bottle  and  stopper  from  each  of  the  last  two 
weights.  This  gives  the  weight  of  equal  volumes  of  water  and 
of  gasoline.  From  these  two  weights  find  the  specific  gravity  of 
gasoline,  i.e.  the  ratio  between  the  weights  of  equal  volumes 
of  gasoline  and  water.  This  is  numerically  equal  to  the  density 

1  The  scale  should  always  be  so  chosen  that  the  curve  will  cover  nearly  the 
entire  page.  Any  number  of  spaces,  however,  or  any  fractional  part  of  a  space 
might  be  used  vertically  or  horizontally  to  represent  a  millimeter  of  pressure 
or  a  centimeter  of  depth. 


18 


LABORATORY  PHYSICS 


of  gasoline,  i.e.   the   number  of  grams  in  1  cc.,  since  1  cc.  of 
water  weighs  1  g.    Record  thus : 

Weight  of  bottle  =  —  g. 

Weight  of  bottle  and  water      = g. 

Weight  of  bottle  and  gasoline  = g. 

.-.  Weight  of  water  = g. 

.-.  Weight  of  gasoline  — g. 

.-.  Density  of  gasoline 

II.  Determination  of  the  pressure  within  the  bottle  B.  Arrange 
two  pressure  gauges,  or  manometers,  as  in  Fig.  13,  gauge  1  being 
filled  with  water,  and  gauge  2  with  gasoline.  Force  air  through 
0  into  the  bottle  B  until  the  gasoline  column 
is  near  the  top.  Then  close  with  the  pinch- 
cock  K  the  rubber  tube  which  connects  the 
bottle  with  the  outside  air. 

As  soon  as  the  levels  of  the  gauges  are 
stationary  measure  with  a  meter  stick  the 
height  of  the  liquid  surfaces  above  the  table 
at  a,  d,  5,  and  e,  measuring  in  each  case  to 
the  lowest  part  of  the  curved  liquid  surface. 
Let  hl  represent  the  difference  in  level  in 
centimeters  between  the  points  a  and  d,  and 
let  7i2  represent  the  difference  between  the 
points  b  and  e.  Let  d1  and  d.2  represent  the 
densities  of  the  liquids  in  1  and  2  respec- 
tively. 

From  each  of  the  relations  p  —  li^d^  and  p  =  A2c?2,  compute  the 
pressure  jo,  in  grams  per  square  centimeter,  existing  within  the 
bottle,  and  see  how  well  the  two  results  agree.  This  will  be 
a  check  on  the  correctness  of  the  density  determination  which 
you  made  in  I.  It  need  scarcely  be  said  that  the  pressure 
acting  upon  each  manometer  is  necessarily  the  same,  since  it  is 
simply  the  pressure  existing  within  the  bottle. 


FIG. 


ARCHIMEDES'  PRINCIPLE  —  DENSITY  OF   SOLIDS     19 


Record  the  results  of  your  measurements  in  the  following 
form  : 


From  table  to  a  = 

From  table  to  d  — 

.-.  A    =  -  cm.. 


cm. 
cm. 


From  table  to  b  = 
From  table  to  e  = 


cm. 
cm. 


Mean  p,  in  grams  per  square  centimeter, 

Per  cent  of  difference  between  pressure  by  1  and  '2      =  - 

III.  Measurement  of  pressure  in  city  gas  mains.  Attach  K  to 
the  gas  cock  and  see  how  good  an  agreement  you  can  obtain 
between  the  two  different  measurements  of  the  gas  pressure 
furnished  by  the  two  manometers. 

Record  III  exactly  as  you  recorded  II. 

Answer  in  your  notebook  the  following  questions  : 

If  the  manometer  tubes  had  had  different  diameters,  would 
the  results  have  been  different?    State  reasons. 
-  Can  you  see  in  II  a  ready  means  of  comparing  the  densities 
of  any  two  liquids?    From  your  results  compare  the  densities  of 
water  and  gasoline  by  this 
method  and  see   how  well  the 
result   agrees  with  that   found 
in  I. 

EXPERIMENT  7 

ARCHIMEDES'  PRINCIPLE  AND 
THE  DENSITY  OF  A  SOLID 

I.  To  test  Archimedes'  prin- 
ciple for  immersed  bodies.  Re- 
move the  left  pan  from  the 
balance  and  replace  it  by  the  counterpoise  c  (Fig.  14)  which  is 
made  as  nearly  as  possible  of  the  same  weight  as  the  pan.  Adjust 
the  balance  by  means  of  the  nut  n  until  the  pointer  stands  at 


FIG.  14 


20  LABORATORY  PHYSICS 

the  middle  mark.  Suspend  an  aluminum  cylinder,  or  any  regu- 
lar solid  body  of  volume  50  cc.-  or  more,  from  the  left  arm  of  the 
balance  and  counterpoise  accurately  with  weights  in  the  opposite 
pan.  Record  this  weight. 

Immerse  the  cylinder  in  water,  as  in  Fig.  14.  Carefully  remove 
all  air  bubbles  and  weigh  again.  From  these  observations  find 
the  loss  of  weight  which  the  body  experiences  when  immersed  in 
water.  Measure  the  dimensions  of  the  cylinder  with  the  microm- 
eter or  vernier  calipers  or  simply  by  wrapping  a  fine  silk  thread 
about  it  say  thirty  times  and  measuring  the  length  of  the 
thread.  Then  compute  the  volume  in  cubic  centimeters. 

Compare  the  loss  of  weight  obtained  above  with  the  weight  of 
the  liquid  displaced  by  the  body  (i.e.  the  volume  of  the  body 
times  the  density  of  the  liquid,  which  is  in  this  case  1). 

Weigh  the  cylinder  when  it  is  immersed  in  a  beaker  of  gaso- 
line and  compare  the  loss  of  weight  with  the  weight  of  the  dis- 
placed liquid,  taking  the  density  of  gasoline  from  the  results  of 
Experiment  6  (I). 

Record  thus  : 

Mean 

Weight  of  cylinder  in  air      = g.   Diameters —  cm. 

Weight  of  cylinder  in  water  = g.   Length  = cm.    .-.Vol.    = cc. 

Loss  of  weight  in  water       = g.   Weight  of  displaced  water     = g. 

Per  cent  of  difference 

Weight  in  gasoline  = g.   Weight  of  displaced  gasoline = g. 

Loss  of  weight  in  gasoline  = g.    Per  cent  of  difference 

State  in  your  notebook  in  your  own  words  the  principle 
which  your  experiment  has  shown  to  be  true. 

II.  To  find  the  density  of  a  solid  heavier  than  water  by  loss 

of  weight  method.     Since  density  is  defined  as  — »  it  is 

volume 

obvious  that  the  most  direct  way  of  determining  the  density  of 
any  regular  solid  is  to  find  its  mass  by  a  weighing  and  its  vol- 
ume by  direct  measurement.  But  it  would  evidently  be  quite 


ARCHIMEDES'  PRINCIPLE  — DENSITY  OF  LIQUIDS      21 

impossible  to  find  in  this  way  the  density  of  an  irregular  body, 
like  a  lump  of  coal,  because  of  the  difficulty  of  measuring  its 
volume.  The  principle  discovered  in  I,  however,  furnishes  a 
very  simple  way  of  finding  this  volume,  since  it  is  only  neces- 
sary to  find  the  loss  of  weight  which  the  body  experiences  in 
water,  in  order  to  find  the  weight  of  an  equal  volume  of  water, 
and  this  is  the  same  as  the  volume  of  the  body,  since  the 
density  of  water  is  1.  We  have,  then, 

weight  in  air 

Density  = ,    &.   , — : 

loss  of  weight  in  water 

Without  making  any  additional  measurements,  find  the  den- 
sity of  the  body  used  in  I,  (a)  by  dividing  the  weight  in  air 
by  the  volume  as  there  computed  from  its  dimensions,  and 
(b)  by  dividing  the  weight  in  air  by  the  volume  of  the  cylinder 
as  found  from  the  loss  of  weight  in  water. 

Find  in  the  latter  way  the  density  of  some  irregular  body, — 
for  example,  a  brass  weight. 

Record  thus : 

(a)  Density  of  aluminum  =  mass  -=-  volume  from  dimensions       =  — 

(fi)   Density  of  aluminum  =  mass  -f-  volume  from  loss  of  weight  = 

Per  cent  of  difference      =  — 

Weight  of  brass  body  in  air  = g. ;  weight  in  water         =  — 

.-.  Density  of  brass  = Accepted  value  =8.4 


EXPERIMENT  8 
ARCHIMEDES'  PRINCIPLE   AND  THE  DENSITY  OF  A   LIQUID 

I.  To  test  Archimedes'  principle  for  floating  bodies.  Place  in 
a  deep  vessel  of  water  (see  Fig.  11,  p.  14)  a  piece  of  thin- walled, 
cylindrical  glass  tubing  about  three  quarters  of  an  inch  in  diam- 
eter, twenty-four  inches  long,  and  loaded  with  shot  at  the  lower 


22  LABORATORY  PHYSICS 

end  (Fig.  15).  (For  the  sake  of  convenience  in  II  it  is  best 
to  load  the  tube  first  in  a  vessel  of  gasoline  until  it  sinks  to 
within  say  2  cm.  of  the  top  and  then  to  transfer  it  with- 
out change  in  the  load  to  the  vessel  of  wate,r.)  Place  a 
rubber  band  about  the  tube  at  the  exact  point  to  which 
it  sinks.  Remove  the  tube  from  the  water,  wipe  it  dry, 
and  then  weigh  it  with  the  contained  shot.  Measure 
the  diameter  of  the  tube  in  four  or  five  different  places, 
and  the  distance  from  the  rubber  band  to  the  bottom. 
From  these  two  measurements  compute  the  volume,  and 
therefore  the  weight,  of  the  water  displaced  by  the  float- 
ing body.  Record  thus : 

First  diam.     = cm.  Length  immersed  = cm. 

Second  diam.  = cm.  Area  of  cross  section  = sq.cm. 

Third  diam.    = cm.  Weight  of  displaced  water  = g. 

Fourth  diam.  = cm.  Weight  of  tube  and  shot   = g. 

Mean  diam.    = cm.  Per  cent  of  difference         = 

Infer  from  your  results  the  general  law  of  flotation 
and  state  it  in  your  notebook. 
Fio  lfi        II.  Density  of  a  liquid  by  the  principle  of  flotation. 

(a)  Constant-weight  hydrometer.  Immerse  the*  tube 
with  its  contents  in  a  vessel  of  gasoline.  Since  the  tube  will 
float  only  when  the  weight  of  the  displaced  liquid  is  equal  to 
the  weight  of  the  floating  body,  and  since  gasoline  is  less 
dense  than  water,  the  tube  must  sink  to  a  greater  depth  in  the 
lighter  liquid  than  it  did  in  water,  e.g.  to  some  point  C.  Place 
a  rubber  band  at  this  point,  and  then  remove  and  measure  the 
length  immersed. 

If  Zj  is  the  length  of  the  tube  immersed  in  water  and  lz  the 
length  immersed  in  gasoline,  then  the  density  of  gasoline  must 
be  Zj/Zj  times  the  density  of  water ;  for  if  A  represents  the  area 
of  the  cross  section  of  the  tube,  the  weight  of  the  water  dis- 
placed by  the  tube  is  Al-^ ;  and  if  d  is  the  density  of  gasoline, 


ARCHIMEDES'  PRINCIPLE  — DENSITY  OF  LIQUIDS     23 

the  weight  of  the  displaced  gasoline  is  Al^d\  and  since  these 
weights  are  equal,  being  both  equal  to  the  weight  of  the  float- 
ing body,  we  have  Al2d  =  Alv  i.e.  d  =  l^  /  l^. 

Test  the  correctness  of  your  result  by  means  of  a  commercial 
constant-weight  hydrometer  (see  Fig.  16). 

(b)    Constant-volume  hydrometer.    Drop  shot  into  a  test  tube 
which  has  been  drawn  out  to  the  shape  shown  in  Fig.  17 
until,  when  immersed  in  gasoline,  it  sinks  to 
the  mark  a  on  the  narrow  part  of  the  stem. 
Remove  the  tube,  dry,  and  weigh  with  the  con- 


tained  shot.  Immerse  in  water,  add  more  shot 
until  the  tube  sinks  to  the  same  mark,  remove, 
dry,  and  weigh  again.  The  volume  of  the  liquid 
displaced  is  the  same  in  the  two  cases,  and  the 
weight  of  this  volume  is  equal  to  the  weight 
of  the  tube  and  its  contents.  The  specific  grav- 
ity or  density  of  the  gasoline  may  therefore  be 


1 


found  at  once,  since  the  data  are  available  for    „ 

FIG.  !<>„-.  .  FlG-  !' 

finding  the  weight  of  a  given  volume  of  gaso- 
line and  the  weight  of  an  equal  volume  of  water.    Compare  the 
results  with  those  obtained  in  («).    Record  as  follows : 

(«)  (6) 

Length  in  water  —  cm.  Weight  in  water  = g. 

Length  in  gasoline  — cm.  Weight  in  gasoline  = g. 

Density  of  gasoline  Density  of  gasoline 

By  hydrometer  of  Fig.  16= Diff .  between  (a)  and  (It)     =  — 

Per  cent  of  difference         = Per  cent  of  error 

State  in  your  notebook  what  two  general  methods  }*ou  have 
discovered  for  finding  the  densities  of  liquids. 

Can  you  see  any  reason  why  a  constant-weight  hydrometer 
made  with  a  narrow  stem  (Fig.  16)  is  a  much  more  accurate 
instrument  for  determining  the  densities  of  liquids  than  a  cylin-" 
drical  constant-weight  hydrometer  like  that  shown  in  Fig.  15  ? 


24 


LABORATORY  PHYSICS 


If  any  convenient  solid  is  weighed  first  in  air,  then  in  water, 
and  then  in  some  other  liquid,  e.g.  gasoline,  the  three  weighings 
will  furnish  data  for  determining  the  density  of  gasoline.  Write 
an  explanation  of  this  in  your  notebook,  and  compute  the  density 
of  gasoline  from  the  weighings  of  this  sort  which  you  made  in 
Experiment  7. 

EXPERIMENT  9 
DENSITY  OF  A  SOLID  LIGHTER  THAN  WATER 

I.  By  weighing  first  in  air  and  then  when  immersed  in  water 
with  the  aid  of  a  sinker.  If  a  body  is  lighter  than  water,  the 
weight  of  an  equal  volume  of  water  may 
be  obtained  with  the  aid  of  a  sinker.  Use 
a  wooden  block  E  (Fig.  18)  which  has 
been  paraffined  so  as  to  prevent  the  ab- 
sorption of  water.  Weigh  the  block  in 
air  and  then  with  the  sinker  attached,  the 
block  being  in  air  and  the  sinker  S  in 
water,  as  shown  in  the  figure.  Lastly, 
weigh  when  the  block  and  sinker  are  both 
under  water.  The  difference  between  the 
second  and  third  weighings  is  evidently 
the  buoyant  effect  of  the  water  on  the 
block  alone,  i.e.  it  is  the  weight  of  the 
water  displaced  by  the  block,  and  hence 
it  is  also  the  volume  of  the  block.  From 
this  difference  and  the  weight  of  the 
block  in  air  obtain  the  density  of  the  wood.  Record  thus : 

Weight  of  block  alone  in  air  —  g. 

Weight  when  block  is  in  air  and  sinker  in  water  — g. 

Weight  when  both  block  and  sinker  are  in  water  = g. 

.-.  Density  of  wood  » 


FIG.  18 


DENSITY  OF  A  SOLID  LIGHTER  THAN  WATEK     25 

Explain  in  your  notebook  how  you  calculated  the  density  of 
wood  and  why  your  method  of  procedure  gives  this  density. 

II.  From  weight,  length,  breadth,  and  thickness  of  block. 
Measure  the  three  dimensions  of  the  block  with  a  meter  stick 
held  on  edge,  as  in  Fig.  2.  From  these  measurements  and  the 
weight  of  the  block,  obtained  in  I,  compute  the  density  of  the 
wood.  Record  thus : 


Length  of  block        = 
Height  of  block 
Thickness  of  block  = 


cm.      .-.  Volume  = 
cm.      .-.  Density  = 


%  of  difference  in  I  and  II  = 


III.  From  the  depth  to  which  the  block  sinks  in  water.  Wax 
a  pin  to  the  end  of  a  metric  rule  ai,  arranged  as  in  Fig.  19,  and 
take  the  reading  of  the  point  on  this 
rule  at  which  it  meets  the  straight 
edge  CD  when  the  pin  point  just 
touches  the  corner  m  of  the  floating 
block.  Then  take  the  reading  on  ab 
when  the  pin  point  just  touches  the 
surface  of  the  water,  say  1  cm.  away 
from  the  edge  of  the  block.  The 
difference  between  these  two  read- 
ings subtracted  from  the  thickness 
of  the  block  would  give  the  distance 
which  the  block  sinks  in  the  liquid,  if  the  surface  of  the  block 
were  accurately  horizontal.  In  order  to  obtain  as  accurate  a 
value  as  possible  for  this  distance,  repeat  the  measurements  at 
each  corner  of  the  block,  and  take  a  mean  of  these  four  differ- 
ences. From  this  mean  difference  find  the  distance  h'  which 
the  block  sinks  in  water.  Then,  from  h'  and  the  thickness  h 
of  the  block,  compute  its  density  d  from  the  relation 


FIG.  19 


26  LABORATORY  PHYSICS 

Record  the  results  of  your  observations  thus : 

First          Second         Third  Fourth 

corner          corner         corner  corner 

Reading  with  pin  touching  water  = cm. cm. cm. —  cm. 

Reading  with  pin  touching  block  = cm. cm. cm. cm. 

Differences  — cm. cm. cm.  cm. 

Mean  difference  = It  = .-.  It'  —  —  -    .-.  d  —  — 

Prove  in  your  notebook  that  the    above  equation   for  the 

7  I 

density  of  the  block,  namely  d  =  — ,  follows  at  once  from  the 

statement  of  Archimedes'  principle  as  applied  to  floating  bodies, 
viz.  "  The  weight  of  the  floating  body  is  equal  to  the  weight  of 
the  liquid  which  it  displaces."  (Remember  that  weight  =  vol- 
ume X  density ;  so  that,  if  A  represent  the  area  of  the  top  of 
the  block,  the  weight  of  the  block  is  Ahd,  while  the  weight 
of  the  displaced  liquid  is  Ah'd',  d'  in  this  case  being  1.) 

Can  you  see  from  your  analysis  any  general  relation  which 
must  always  exist  between  the  density  of  a  body  floating  on 
water,  the  volume  of  the  body,  and  the  fraction  of  the  volume 
which  is  beneath  the  surface? 


EXPERIMENT  10 

THE   RELATION  BETWEEN   THE   PRESSURE   AND  VOLUME 

OF  A  GIVEN  MASS  OF   GAS  AT  CONSTANT 

TEMPERATURE 

I.  Verification  of  Boyle's  law.  The  object  of  this  experiment 
is  to  vary  the  volume  of  a  small  quantity  of  air  AD  (Fig.  20, 1), 
confined  in  a  barometer  tube,  by  varying  the  pressure  to  which 
it  is  subjected,  and  to  find  how  this  volume  changes  as  we 
double,  treble,  quadruple,  etc.,  the  pressure. 

First  read  the  barometer  and  record  its  height  in  centimeters  ; 
then,  by  means  of  a  clamp  (7,  hold  in  the  position  1  (Fig.  20)  a 


BOYLE'S  LAW 


27 


barometer  tube  which  is  closed  at  the  upper  end  and  open  at 
the  lower  end,  and  which  contains  a  mercury  column  AS  and 
the  thread  of  air  AD.1  Measure  carefully  the  length  AD  of  the 


confined  body  of  air.  Since  the  cross  section  of  the  tube  is 
everywhere  the  same,  the  volume  of  the  confined  air  will  always 
be  proportional  to  its  length  ;  hence  we  shall  call  the  length 
AD  volume  1,  and  shall  denote  it  by  l\. 

1  To  construct  tubes  of  this  sort  pieces  of  barometer  tubing  should  be  chosen 
which  are  from  1  mm.  to  1.5  mm.  in  bore  and  110  cm.  long.  They  should  be 
cleaned  by  pouring  through  them  a  hot  solution  of  potassium  bichromate  in 


28  LABORATORY  PHYSICS 

Next  measure  the  length  of  the  mercury  column  AB  in  centi- 
meters. The  barometric  height  minus  this  length  AB  is  obvi- 
ously the  pressure,  measured  in  centimeters  of  mercury,  to 
which  the  air  Fj  is  subjected.  Call  this  pressure  Pr 

Incline  the  tube  slowly  until  the  volume  T2  (see  Fig.  20,  2)  of 
the  inclosed  air  is  one  half  of  the  original  volume  Fr  Now  meas- 
ure the  heights  of  the  points  A  and  B  above  the  table  and  sub- 
tract the  difference  AB'  from  the  barometric  height,  thus  getting 
P2,  the  pressure  corresponding  to  the  volume  F2.  (The  reason 
for  this  procedure  will  be  clear  when  it  is  remembered  that 
pressure  in  liquids  depends  simply  upon  difference  in  horizontal 
levels.1} 

Place  the  tube  successively  in  positions  3,  4,  5  (see  Fig.  20) 
such  that  the  volume  of  the  inclosed  air  shall  be  1/3,  1/4,  1/5, 
and,  if  possible,  1/6  of  the  original  volume.  Measure  in  each 
case  the  heights  of  the  ends  A  and  B  of  the  mercury  column 
from  the  table  top  and  compute  the  pressures  corresponding  to 
each  volume.  (Remember  that  the  pressure  on  the  confined  air 
is  less  than  the  barometric  pressure  if  the  open  end  of  the  tube 
is  lower  than  the  closed  end,  and  greater  than  the  barometric 
pressure  if  the  open  end  is  above  the  closed  end.) 

strong  sulphuric  acid.  They  should  then  be  rinsed  first  with  distilled  water, 
then  with  clean  alcohol,  and  finally  dried  with  a  current  of  air  from  a  bellows. 
These  tubes  may  be  filled  by  sinking  them  in  a  larger  tube  containing  perfectly 
clean  mercury  until  the  mercury  rises  in  the  capillary  bore  to  within  12  or 
15  cm.  of  the  top,  and  then  sealing  the  top  with  hard  wax  and  withdrawing ; 
or,  again,  the  tube  may  be  laid  horizontally  and  a  piece  of  gum  tubing  attached 
to  one  end  and  clean  mercury  poured  into  this  tubing  until  it  approaches  to 
within  5  or  6  cm.  of  the  other  end,  when  the  sealing  should  be  done. 

JThe  proof  that  this  is  indeed  the  case  is  found  in  the  familiar  fact  that  water 
will  stand  at  the  same  level  in  two  vessels  connecting  at  the  bottom  and  consist- 
ing, the  one  of  a  long  inclined  tube,  the  other  of  a  short  vertical  one.  If  the 
pressure  at  the  bottom  of  the  longer  tube  were  the  greater,  the  water  would,  of 
course,  have  to  stand  higher  in  the  shorter  tube. 


BOYLE'S  LAW 


29 


Record  as  follows : 


POSI- 
TION 

VOLUME 
OF  CON- 
FIXED 
Am 

HEIGHT 

OF  A 
ABOVE 

TABLE 

HEIGHT 

OF  B 
ABOVE 

TABLE 

DIFFER- 
ENCE 

BARO- 
METRIC; 
HEIGHT 

PRES- 
SURE 

PRES- 
SURE 

TIMES 

VOLUME 

DIFFER- 
ENCE 

FROM 

MEAN 

rv 

1 

2 

3 

4 

5 

II.  Graphical  representation  of  an  inverse  proportion.  When 
two  quantities  are  related  in  the  way  in  which  P  and  V  are 
found  to  be  related  above,  i.e.  when  making  P  two,  three,  or 
four  times  as  great  makes  V  1/2,  1/3,  or  1/4  as  great,  one 
quantity  is  said  to  be  inversely  proportional  to  the  other,  or  to 
vary  inversely  with  the  other.  It  will  be  seen  from  the  next  to 
the  last  column  that  the  product  of  two  quantities  which  vary 
in  this  way  is  always  constant.  Hence,  if  Pv  P2,  P3,  etc.,  represent 
the  pressures  corresponding  to  the  volumes  Vv  F2,  F3,  etc.,  then 

pz      v\      A      vi 
or,  more  simply,  PF  =  constant. 

This  is  the  analytic  or  algebraic  way  of  expressing  the  fact  that 
P  and  V  are  inversely  proportional  to  each  other. 

To  find  the  graph  or  curve  which  represents  an  inverse  pro- 
portion, plot  on  a  sheet  of  coordinate  paper,  precisely  as  in 


30  LABORATORY  PHYSICS 

Experiment  5,  the  pressures  in  the  table  above  as  horizontal 
distances  and  the  corresponding  volumes  as  vertical  distances. 
Utilizing  the  law  discovered  experimentally  above,  compute  the 
pressures  which  would  correspond  to  two,  three,  and  four  times 
the  original  volume,  and  the  volumes  corresponding  to  two, 
three,  and  four  times  the  greatest  pressure,  and  plot  as  part  of 
the  same  curve  not  only  the  points  corresponding  to  the  observed 
values  but  also  those  corresponding  to  these  computed  values 
of  the  pressure  and  volume.  Select  your  scale  so  that  the  curve 
will  just  nicely  fill  a  sheet  of  coordinate  paper. 

This  curve  is  an  hyperbola.  Its  two  arms  approach  nearer 
and  nearer  to  the  axes  OX  and  OF,  but  the  curve  can  never 
touch  these  arms,  for  no  matter  how  great  the  pressure  may 
become,  the  volume  will  never  become  zero,  and  no  matter  how 
great  the  volume  may  become,  the  pressure  will  never  be  quite 
zero.  The  lines  which  an  hyperbola  approaches  indefinitely, 
without  ever  exactly  reaching,  are  called  the  asymptotes  of  the 
hyperbola.  In  this  case  the  asymptotes  are  the  coordinate  axes 
OT  and  OY. 

Summarize  in  the  notebook  the  results  of  the  experiment, 
stating  first  in  words  the  relation  which  has  been  found  to 
exist  between  pressure  and  volume,  then  expressing  this  rela- 
tion in  the  form  of  an  equation,  and  then  stating  what  sort  of 
curve  the  experiment  has  shown  to  be  the  graph  of  this  type 
of  relationship. 

EXPERIMENT   11 

COOLING  BY  EVAPORATION;  SATURATION;  DEW-POINT; 
FREEZING  BY  EVAPORATION 

I.  Cooling  by  evaporation.  Let  three  4-oz.  bottles,  one  half 
full  of  ether,  one  half  full  of  alcohol,  and  one  half  full  of  water, 
be  provided.  The  bottles  should  be  closed  with  small  corks  and 


HYGROMETRY  31 

should  have  been  standing  in  the  room  long  enough  to  acquire 
room  temperature. 

Holding  a  thermometer  by  a  string  attached  to  the  upper  end, 
swing  it  back  and  forth  through  the  air  until  its  reading  is  con- 
stant. Record  this  reading  as  the  room  temperature.  Insert  the 
thermometer  in  the  ether  bottle,  pushing  the  bulb  down  beneath 
the  surface  of  the  liquid.  After  half  a  minute  record  the  reading 
as  the  temperature  of  the  ether  in  the  closed  bottle.  In  the 
same  way  take  the  temperatures  of  the  alcohol  and  water. 

Pour  into  small  porcelain  evaporating  dishes  enough  of  each 
liquid  to  cover  the  bulb  of  the  thermometer.  Pour  about  the 
same  amount  of  ether  into  an  open  test  tube  (or  the  metal  tube 
of  Fig.  21),  and  set  it  aside  in  a  beaker  or  other  convenient 
support.  Place  the  thermometer  in  the  evaporating  dish  which 
contains  the  ether,  and,  keeping  the  stem  inclined  so  that  the 
bulb  is  always  covered,  watch  the  temperature  until  it  ceases  to 
change,  and  then  record.  Take  in  succession  the  temperatures 
of  the  alcohol  and  of  the  water  in  the  evaporating  dishes,  and 
of  the  ether  in  the  test  tube.  Record  thus : 

Temperature  in  room 

Temperature  in  bottle  of  ether 

Temperature  in  bottle  of  alcohol 

Temperature  in  bottle  of  water 

Temperature  of  ether  in  evaporating  dish     =  - 

Temperature  of  alcohol  in  evaporating  dish  =  — 

Temperature  of  water  in  evaporating  dish     = 

Temperature  of  ether  in  test  tube 

State  in  your  notebook  what  effect  your  experiments  have 
shown  evaporation  to  have  upon  the  temperature  of  the  evapo- 
rating body.  Explain,  if  you  can,  why  the  temperature  of  the 
ether  in  the  test  tube  was  different  from  that  in  the  evaporating 
dish.  Put  a  drop  of  ether,  of  alcohol,  and  of  water  upon  the 
hand  and  notice  the  order  in  which  they  disappear.  Explain 


32  LABORATORY  PHYSICS 

with  the  aid  of  this  experiment  and  the  answer  to  the  first  ques- 
tion why  the  ether  in  the  evaporating  dish  had  a  lower  temper- 
ature than  the  alcohol,  and  the  alcohol  a  lower  temperature 
than  the  water. 

When  a  body  is  below  room  temperature  it  is  continually 
receiving  heat  from  the  room.  When  the  liquids  in  the  evapo- 
rating dishes  had  reached  a  constant  temperature,  what  relation 
existed  between  the  amount  of  heat  which  they  lost  per  second 
by  evaporation  and  the  amount  which  they  received  per  second 
from  the  room? 

'  II.  Saturation.  From  the  above  readings  of  the  room  tem- 
perature and  the  temperature  of  the  liquids  in  the  closed  bottles, 
can  you  draw  any  inference  as  to  whether  or  not  any  evapora- 
tion was  going  on  from  the  surfaces  of  the  liquids  in  the 
closed  bottles?  A  space  in  which  evaporation  will  no  longer 
take  place  from  the  surface  of  a  given  liquid  placed  within 
the  space  is  said  to  be  saturated  with  the  vapor  of  the  liquid. 
This  means  simply  that  the  space  already  contains  as  much  of 
the  vapor  of  the  liquid  as  it  is  capable  of  holding  at  the  given 
temperature. 

Cover  the  bulb  of  the  thermometer  with  a  bit  of  absorbent 
cotton,  dip  it  into  the  bottle  of  ether,  and  then  lift  it  so  that 
the  bulb  and  cotton  are  above  the  surface  of  the  ether,  but  still 
in  the  bottle.  Watch  the  temperature  for  a  minute  or  two,  and 
then  record.  Transfer  the  covered  bulb  from  the  bottle  to  the  test 
tube  and  hold  it  there  above  the  surface.  After  a  minute  or  two 
record  the  temperature.  Lift  the  covered  bulb  out  into  the  air 
and  record  the  temperature  after  it  has  become  constant.  What 
do  you  learn  from  this  experiment  regarding  the  temperature 
which  a  thermometer  surrounded  with  a  cloth  soaked  in  a  liquid 
will  maintain  in  a  space  which  is  saturated  with  the  vapor  of 
the  liquid?  in  a  space  which  is  partially  saturated?  in  a  space 
which  is  free  from  this  vapor,  i.e.  which  is  dry? 


HYGEOMETRY  33 

Wrap  some  fresh  cotton  about  the  bulb  of  the  thermometer, 
and  dip  it  into  the  bottle  of  water ;  then  remove  the  thermom- 
eter and  swing  it  in  the  room  until  its  reading  becomes  con- 
stant. Record.  Would  this  reading  be  any  different  if  there 
were  no  water  vapor  already  in  the  room  ?  What  would  it  be 
if  the  air  were  already  saturated  with  water  vapor?  Can  you 
see,  then,  how  the  difference  between  the  readings  of  a  ther- 
mometer whose  bulb  is  kept  dry  and  one  whose  bulb  is  kept 
moist  gives  us  some  information  regarding  the  dryness  of  the 
atmosphere  ? 

III.  Dew-point.  The  amount  of  vapor  which  a  given  space 
can  hold  is  found  to  decrease  rapidly  as  the  temperature 
decreases.  Hence,  if  we  lower  the 
temperature  of  a  space  which  is 
already  saturated  with  any  vapor,  a 
part  of  it  condenses.  If  we  lower 
the  temperature  of  a  space  which 
is  not  saturated,  but  which  contains 
some  vapor,  nothing  happens  until 
the  temperature  is  reached  at  which 
the  amount  of  vapor  which  already 
exists  in  the  space  is  the  amount  Fi 

which  saturates  it.    Then  condensa- 
tion begins.    The  temperature  at  which  water  vapor  begins  to  con- 
dense out  of  the  atmosphere  as  the  temperature  is  lowered,  is  called 
the  dew-point.    It  varies  of  course  from  day  to  day,  depending 
upon  how  much  water  vapor  exists  in  the  atmosphere. 

Fill  the  polished  metal  tube l  of  Fig.  21  two  thirds  full  of 
ether,  and  force  air  very  gently  through  it  by  squeezing  the  bulb. 

1  This  experiment  can  be  performed  with  almost  as  good  success  by  simply 
dropping  bits  of  ice  slowly  into  water  contained  in  a  polished  vessel,  and  noting 
the  temperature  at  which,  with  continual  stirring,  the  cloud  appears  on  the  out- 
side. If  the  dew-point  is  below  zero,  salt  should  be  added  bit  by  bit  to  the  iced 
water  until  the  cloud  appears. 


34 


LABORATOBY  PHYSICS 


This  process  facilitates  cooling,  since  it  increa'ses  enormously 
the  evaporating  surface,  every  bubble  having  a  large  surface 
into  which  evaporation  can  take  place.  The  temperature  exist- 
ing within  the  tube  when  the  first  cloudiness  begins  to  appear 
upon  the  polished  surface  is  the  dew-point,  for  it  is  the  tem- 
perature at  which  the  layers  of  air  in  contact  with  the  tube 
become  saturated  and  begin  to  deposit  their  moisture.  As  soon 
as  this  cloudiness  is  noticed  take  the  reading  of  the  thermometer, 


re.                 P 

rc. 

P 

t°c. 

P 

-10° 

2.2 

0° 

6.5 

19° 

16.3 

-  9° 

2.3 

6° 

7.0 

20° 

17.4 

-   8° 

2.5 

7° 

7.5 

21° 

18.5 

-    7° 

2.7 

8° 

8.0 

22° 

19.6 

-    6° 

2.9 

9° 

8.5 

23° 

20.9 

-    5° 

3.2 

10° 

9.1 

24° 

22.2 

-    4° 

3.4 

11° 

9.8 

25° 

23.5 

-   3° 

3.7 

12° 

10.4 

26° 

25.0 

-    2° 

3.9 

13° 

11.1 

27° 

26.5 

-    1° 

4.2 

14° 

11.9 

28° 

28.1 

0° 

4.6 

15° 

12.7 

29° 

29.7 

1° 

4.9 

16° 

13.5 

30° 

31.5 

2° 

6.3 

17° 

14.4 

35° 

41.8 

3° 

5.7 

18° 

15.3 

40°                  54.9 

4° 

6.1 

45°                  71.4 

1 

and  then  stop  the  current  and  notice  the  temperature  at  which 
the  cloudiness  disappears.  Take  pains  in  these  experiments  not 
to  breathe  upon  the  polished  surface.  Repeat  the  whole  opera- 
tion until  the  temperatures  of  appearance  and  disappearance  do 
not  differ  by  more  than  1°.  Take  the  mean  of  the  two  tem- 
peratures as  the  dew-point. 

From  the  dew-point  and  the  accompanying  table  find  the 
humidity  of  the  atmosphere.  This  is  the  ratio  between  the 
amount  of  moisture  in  the  atmosphere  at  the  time  of  the  ex- 
periment and  the  total  amount  which  it  is  capable  of  holding 


HOOKE'S  LAW 


35 


at  the  temperature  of  the  room.  It  is  found  by  dividing  the 
pressure  of  saturated  water  vapor  at  the  temperature  of  the 
dew-point  by  the  pressure  of  saturated  water  vapor  at  the  tem- 
perature of  the  room  (see  table  on  page  34 ).1 

IV.  Freezing  by  evaporation.  Place  a  few  drops  of  water  upon 
the  table  and  set  the  polished  metal  tube  containing  ether  upon  it. 
Force  air  through  the  ether  rapidly  and  see  if  you  can  freeze  the 
tube  to  the  table. 

EXPERIMENT  12 

RELATION   BETWEEN   FORCE  ACTING  UPON  AN  ELASTIC 
BODY  AND   THE   DISPLACEMENT   PRODUCED 

(If yoke's  law) 

I.  Stretching.  Set  up  a  steel  spring  S  and  mirror  scale  M,  in 
the  manner  shown  in  Fig.  22. 

Take  the  reading  of  the  index  upon  the  scale  when  only  the 
weight  holder  hangs  from  the  spring.  In  so 
doing  place  the  eye  so  that  "the  image  of  the 
tip  of  the  pointer  p,  as  seen  in  the  mirror,  is 
exactly  in  line  with  the  tip  of  the  pointer 
itself.  Record  the  position  at  which  the  line  of 
sight  crosses  the  mirror  scale,  reading  to  the 
nearest  tenth  millimeter  (this  tenth  millimeter 
place  being,  of  course,  an  estimate). 

Increase  the  weight  upon  the  pan  100  g.  at 
a  time  until  it  has  reached  a  total  of  400  g.,  and 
take  the  reading  on  the  scale  after  each  addition. 

Then  remove  the  weights  100  g.  at  a  time  and 
take  the  corresponding  readings. 

Tabulate  results  as  indicated  on  page  36. 

1  The  table  shows  the  pressure  P,  in  millimeters  of  mercury,  of  water  vapor 
saturated  at  temperature  t°  C. 


FIG.  22 


36  LABORATORY  PHYSICS    • 

II.  Bending.    Set  up  the  mirror  scale  behind  the  middle  of  a 
thin  wooden  or  steel  rod  supported  as  in  Fig.  23,  and  take 


FIG.  23 

again  a  set  of  readings  like  those  in  I,  the  index  being  now  the 
point  of  a  pin  stuck  with  wax  to  the  middle  of  the  rod. 
Tabulate  results  of  all  observations  as  follows  : 

Spring  Differences  Rod  Differences 

Pan  reading  = 

100-g.  reading  =— — 

200-g.  reading  =  — 

300-g.  reading  = 

400-g.  reading  = — 

300-g.  reading  = — 

200-g.  reading  =  — 

100-g.  reading  =  — 

Pan  reading  —  — 

State  in  your  own  words  in  the  notebook  the  law  which  the 
above  study  of  two  different  sorts  of  elastic  displacement  has 
shown  to  exist  between  the  distorting  force  F  and  the  displace- 
ment D  which  this  force  produces. 

State  this  result  in  the  form  of  an  equation. 

Finally,  put  the  results  of  each  experiment  into  graphical 
form,  letting  one  space  in  the  direction  OY  (see  Fig.  12)  rep- 
resent 15  mm.  of  displacement  from  the  "pan  reading,"  and 
one  space  in  the  direction  OX,  10  g.  of  weight  added  to  the 


COEFFICIENT  OF  EXPANSION  OF  AIR 


37 


pan.  For  each  set  of  observations  draw  with  a  ruler  straight 
lines  which  shall  come  as  near  as  possible  to  touching  all  the 
points  located. 

EXPERIMENT  13 
COEFFICIENT  OF  EXPANSION  OF  AIR 

A  and  B  in  this  experiment  are  intended  as  alternatives,  the  choice 
depending  upon  equipment.  It  is  interesting,  however,  to  have  a  part  of 
the  class  perform  A  and  a  part  B,  and  then  to  let  them  compare  results. 

A.  Pressure  coefficient  of  expansion.  When  a  body  of  gas  is 
heated  in  a  closed  vessel  the  volume  of  which  is  kept  constant, 
the  pressure  which  the  gas  exerts  against  the  walls  of  the  vessel 
increases  as  the  temperature  rises.  The  ratio 
between  the  increase  in  pressure  per  degree 
and  the  pressure  which  the  gas  exerts  at  0°C. 
is  called  the  pressure  coefficient  of  expansion 
of  the  gas.  For  example,  if  Pt  represents  the 
pressure  at  a  temperature  of  t°C.  and  P0  the 
pressure  at  0°C.,  then  the  increase  in  pressure 
has  been  Pt  —  P0,  the  increase  per  degree  has 

been  — 9 ,  and  the  pressure  coefficient  c  is 

this  increase  divided  by  PQ.    Thus, 


FIG.  24 

To  find  this  coefficient  experimentally,  first 

read  the  barometer.  Then,  before  attaching  the  bulb  B,  adjust 
the  arms  a  and  b  (Fig.  24)  until  the  mercury  in  each  stands, 
say,  5  cm.  above  the  bottom  of  the  scale  S,  the  distance  from 
the  bottom  of  S  to  the  point  of  attachment  of  the  rubber  tub- 
ing to  the  arm  b  being  at  least  30  cm.,  and  the  distance  from 


38  LABORATORY  PHYSICS 

the  mercury  surface  in  a  to  the  scratch  m  on  the  tube  a  being 
about  4  cm. 

See  that  a  few  drops  of  concentrated  sulphuric  acid  are 
inserted  in  B  in  order  to  keep  the  inclosed  air  perfectly  dry ; 
then  attach  B  as  in  the  figure,  with  a  bit  of  thick-walled  gum- 
rubber  tubing,  and  pack  wet  snow  or  crushed  ice  about  it  in  a 
vessel  V  until  B  is  completely  covered. 

Raise  the  arm  b  until  the  mercury  in  a  is  just  opposite  the 
scratch  ?n,  tapping  a  gently  with  a  pencil  to  prevent  sticking 
of  the  mercury.  Wait  two  or  three  minutes  to  make  sure  that 
the  air  in  B  has  reached  the  temperature  of  the  ice,  and  then 
adjust  again  to  the  scratch  m  and  read  on  the  scale  S  the  levels 
in  both  a  and  b. 

Put  the  bulb  into  the  steam  generator  shown  in  Fig.  25,  and 
boil  the  water.  Adjust  the  arm  b  until  the  level  in  a  is  again  at 
m ;  tap  and  again  read  the  level  of  the  mercury  in  b. 

Immediately  after  this  reading  loiver  the  arm  b  to  its  first  position, 
so  that  the  mercury  may  not  be  drawn  over  into  B  as  the  bulb  cooh. 

The  difference  between  the  two  readings  in  b  represents  the 
increase  in  the  pressure  exerted  by  the  gas  in  B  as  the  tempera- 
ture was  raised  from  0°C.  to  100°C.;  i.e.  this  difference  is  Pt  -  PQ 
of  our  equation,  t  being  in  this  case  100°.  The  pressure  in  B  at 
0°C.,  namely  P0,  is  simply  the  barometric  height  less  the  differ- 
ence between  the  mercury  levels  in  a  and  b  at  zero. 

Record  your  results  in  systematic  form,  including  a  statement 
of  the  per  cent  by  which  your  result  differs  from  the  accepted 
value  of  this  constant,  namely  .00367,  or  1/273. 

State  in  your  own  way  in  your  notebook  exactly  what  this 
quantity  is  which  you  have  found  above,  and  which  you  call  the 
"  pressure  coefficient  of  expansion." 

What  per  cent  of  error  would  have  been  introduced  into 
your  numerator,  JP100  —  JP0,  and  therefore  into  your  result  by 
an  error  of  half  a  millimeter  in  reading  either  of  the  levels  in  b  ? 


COEFFICIENT  OF  EXPANSION  OF  AIE  39 

If  the  boiling  point  of  water  on  the  day  of  your  experiment 
were  99.5°,  instead  of  100°,  what  per  cent  of  error  would  you 
have  introduced  into  your  result  by  calling  it  100°?  On  the 
whole,  is  your  result  as  accurate  as  you  could  have  expected  in 
view  of  such  sources  of  error  as  you  can  see  ? 

B.  Volume  coefficient  of  expansion.  When  a  confined  body 
of  gas  is  kept  under  constant  pressure  and  heated,  it  follows, 
from  Boyle's  law,  that  its  volume  must  increase  at  the  same 
rate  at  which  its  pressure  would  increase  if  the  volume  were 
kept  constant.  The  ratio  between  the  increase  in  volume  per 
degree  and  the  volume  at  0°C.  is  called  the  volume  coefficient  of 
expansion;  i.e.  if  F100  and  F0  represent  the  volumes  at  100°C. 
and  0°C.  respectively,  then  the  volume  coefficient  c  is  given  by 
the  equation 


This  coefficient  may  be  defined  as  the  expansion  at  0°C.  per 
cubic  centimeter  per  degree.  It  should  be  the  same  as  the  pres- 
sure coefficient  discussed  above. 

To  find  it  experimentally  let  a  thread  of  dry  air  about  23  cm. 
long  be  confined  by  a  mercury  index  2  cm.  or  3  cm.  long  in  a 
piece  of  barometer  tubing  which  is  sealed  at  one  end  and  is 
about  40  cm.  long.1 

First  measure  carefully  and  record  the  length  of  the  index 
and  the  total  length  of  the  bore,  allowing  as  best  you  can  for  the 
fact  that  the  bore  is  not  quite  uniform  very  near  the  closed  end. 

1  To  make  such  tubes  take  barometer  tubing  of  1.5-mm.  bore,  clean  it  with 
hot  aqua  regia,  or  a  hot  solution  of  potassium  bichromate  in  strong  sulphuric 
acid,  then  rinse  with  distilled  water,  and  dry  by  gently  heating  while  a  current 
of  air  passes  first  through  a  calcium  chloride  drying  tube,  and  then  through  the 
barometer  tube.  By  sucking  through  the  drying  apparatus  draw  a  thread  of 
mercury  about  2  cm.  long  into  one  end  of  the  tube,  shake  it  to  within  23  cm. 
of  the  other  end,  and  then  detach  from  the  drying  apparatus  and  quickly  seal 
this  latter  end  in  a  Bunsen  flame. 


40  LABORATORY  PHYSICS 

Then  stand  the  tube  upright,  closed  end  down,  in  a  battery  jar, 
and  pack  wet  snow  about  it  up  to  the  index.  Tap  the  tube  with 
a  pencil,  and  then  measure  from  the  top  of  the  tube  to  the  top 
of  the  index.  Remove  the  tube  and  push  it  through  the  hole 
in  the  cork  which  closes  the  steam  generator  of  Figs.  25  and  36. 
After  the  steam  has  been  issuing  from  the  upper  vent  for  a 
minute  or  two,  adjust  the  height  of  the  tube  in  the  cork  so  that 
the  upper  end  of  the  index  is  just  on  a  level  with  the  top  of  the 
cork,  and  then  measure  from  the  top  of  the  tube  to  the  top  of  the 
cork.  Since  the  tube  is  of  approximately  uniform  bore,  you 
may  take  the  difference  between  the  last  two  measurements  as 
F100  —  FQ.  From  the  first  three  readings  find  the  length  of  the 
thread  of  air  at  0°C.  and  call  it  VQ.  The  following  are  typical 
observations  made  by  a  student. 

Length  of  index  =  18.0mm. 

Length  of  bore  =  476.5  mm. 

From  top  to  index  at  0°  C.  =  251.0  mm. 

From  top  to  index  at  100°C.  =  174.5  mm. 

•'•  FIOO  -  Vo  =  (251-  -  1 74.5)  =  76.5  mm, 

F0  =  476.5  -  (251.  +  18)  =  207.5  mm. 

.-.  c  ^  =  .00369. 

Per  cent  of  departure  from  accepted  value  (.00367)  =  .6. 

Is  your  error  larger  than  would  be  accounted  for  by  an  error 
of,  say,  1  mm.  in  measuring  ( F100  —  V0)  ? 

If  so,  it  is  probable  either  that  the  bore  is  not  uniform,  or 
else  that  the  confined  air  is  not  thoroughly  dry. 


EXPERIMENT  14 
COEFFICIENT  OF  EXPANSION  OF  BRASS 

The  coefficient  of  expansion  of  a  solid  is  equal  to  that  frac- 
tional part  of  its  length  which  it  increases  when  heated  1°, 
i.e.  it  is  the  expansion  per  centimeter  per  degree.  Thus,  if  f3 


COEFFICIENT  OF  EXPANSION  OF  BRASS  41 

represent  the  length  at  a  temperature  £2,  and  ^  at  a  temperature 
tv  the  coefficient  k  is  given  by 


It  may  be  determined  experimentally  by  the  apparatus  shown 
in  Fig.  25. 

A  shallow  transverse  groove  is  filed  at  some  point  c  (Fig.  25) 
near  one  end  of  a  piece  of  brass  tubing  about  a  meter  long  and 
a  centimeter  in  diameter. 

Place  the  tube  upon  two  wooden  blocks  A  and  B,  so  that  the 
groove  rests  upon  a  sharp  metal  edge  attached  to  A,  while  the 


FIG.  25 


other  end  is  supported  by  a  piece  of  glass  or  brass  tubing  b 
about  6  mm.  in  diameter,  which  in  turn  rests  upon  a  smooth 
glass  plate  waxed  to  the  top  of  B.  To  one  end  of  the  glass  rod 
b  is  attached  by  means  of  sealing  wax  a  pointer  p  about  20  cm. 
long.  When  the  brass  rod  is  heated  its  expansion  causes  b  to 
roll  forward,  and  this  produces  a  motion  of  the  end  of  the 
pointer  p  over  the  mirror  scale  s. 

Attach  the  tube,  as  in  the  figure,  to  a  steam  boiler  containing 
at  first  only  cold  water.  Then  insert  a  thermometer  into  the 
open  end  o  of  the  brass  tube. 

Give  the  thermometer  three  or  four  minutes  to  take  up  the 
temperature  of  the  tube  ;  then  read,  record,  and  replace  it 


42  LABOKATORY  PHYSICS 

Record  the  position  of  the  tip  of  the  pointer  upon  the  mirror 
scale,  estimating  very  carefully  to  tenths  of  a  millimeter.  In 
taking  this  reading  sight  (as  always)  across  the  image  of  the 
pointer  and  the  pointer  itself. 

Apply  heat  to  the  boiler  until  steam  passes  rapidly  through 
the  tube.  If  the  current  of  steam  is  sufficiently  strong,  the 
brass  tube  will  not  need  a  nonconducting  covering.  Neverthe- 

less  it  is  generally 
advisable  before 
beginning  the  ex- 
periment  to  roll  up 
a  paper  tube  about 

\\  cm.  in  diameter,  and  to  slip  it  over  the  tube  between  c  and  I 
in  order  to  minimize  heat  losses. 

After  steam  has  been  issuing  from  o  for  one  or  two  minutes, 
take  again  the  reading  of  the  pointer  p  upon  the  scale  «. 

Take  the  reading  of  the  thermometer  as  it  lies  in  the  tube 
surrounded  by  the  steam  escaping  from  o. 

Measure  with  a  meter  stick  the  distance  between  the  knife- 
edge  c  and  the  middle  of  the  rod  b. 

Measure  also  with  the  meter  stick  the  length  of  the  pointer 
p  from  its  tip  to  the  middle  of  b. 

Measure  with  the  micrometer  caliper  the  diameter  of  6,  taking 
readings  upon  at  least  three  different  diameters.  This  measure- 
ment should  be  made  to  within  a  hundredth  of  a  millimeter  at 
the  least.  If  the  calipers  are  not  available,  wrap  a  fine  linen 
thread  ten  or  twenty  times  around  5,  measure  the  length  of  the 
thread,  and  from  this  compute  the  diameter. 

To  find  the  amount  of  expansion  of  the  brass  tube,  divide  the 
difference  in  the  pointer  readings  on  s  by  the  ratio  of  the  length 
of  the  pointer  to  the  diameter  of  the  glass  rod.  The  reason  for 
this  can  be  seen  from  Fig.  26.  At  any  given  instant  the  rod  is 
rotating  about  its  lowest  point  d.  The  line  ef  represents  the 


COEFFICIENT  OF  EXPANSION  OF  BKASS  43 

distance  through  which  the  end  of  the  pointer  moves  while  the 
top  of  the  rod  is  moving  through  a  distance  ab ;  but  from 
similar  triangles 

ab      ef       .     •        ,         ,      de     . 
—  =-f,     i.e.      ab  =  ef+  —  . 
ad      de  ad 

From  the  expansion  of  the  brass  tube,  its  length  between  c 
and  b,  and  its  change  in  temperature,  compute  the  coefficient  of 
expansion  of  the  tube,  i.e.  the  fractional  part  of  its  own  length 
by  which  that  part  of  the  tube  between  c  and  b  expands  when 
heated  1°C. 

If  time  permit,  take  out  the  brass  tube,  cool  it  with  tap  water 
to  about  the  temperature  of  the  room,  and  repeat  the  experiment. 
Take  the  mean  of  the  two  trials  as  the  value  of  k. 

In  calculating  be  sure  that  you  express  all  length  measure- 
ments in  the  same  units,  i.e.  all  in  centimeters,  or  all  in  milli- 
meters ;  not  part  in  centimeters  and  part  in  millimeters. 

Tabulate  as  follows : 

First     Second  „          ^Prnv>li 

Trial  tempera- tempera-  Differ-  r™  ,  ™    Differ-  Length  Diarne-   Coeffi- 

turc  of    tureof  ence        on  gy     on  s       ence      °f cb   terofb     cient 

rod          rod 
•j  

Mean  value  of  k •   = 
Accepted  value     =  .0000187 
Per  cent  of  error  =.    - 

Express  in  words  the  equation  on  page  41. 

What  per  cent  of  error  did  you  introduce  into  the  measure- 
ment of  the  motion  of  the  pointer  over  the  scale,  if  you  made  a 
mistake  of  0.2  mm.  in  estimating  either  position  of  the  pointer? 

What  per  cent  is  introduced  into  the  result  if  the  mean  tem- 
perature of  the  tube  is  1°  lower  than  that  of  the  steam? 

Are  these  errors  greater  or  less  than  the  observed  error? 


44  LABORATORY  PHYSICS 

EXPERIMENT  15 
THE  PRINCIPLE  OF  MOMENTS 

Slip  the  meter  bar  AB  through  the  sliding  knife-edge  sup- 
port C  (Fig.  27)  until  it  will  rest  exactly  horizontally  when 
the  knife-edge  rests  upon  the  glass  surfaces  of  the  wooden 
frame/.  See  that  C  is  clamped  firmly  to  the  bar,  read  the  posi- 
tion of  the  knife-edge  on  the  bar,  and  then  proceed  as  follows. 

(a)  By  means  of  thread  hang  a  100-g.  weight  W^  from  a  point 
near  one  end  of  the  beam  and  find  the  point  at  which  a  200-g. 


FIG.  27 


weight  Wz  must  be  hung  on  the  other  side  in  order  that  the  bar 
may  rest  again  exactly  horizontally.  Take  the  product  of  each 
weight  by  its  distance  from  the  fulcrum.  What  relation  do  you 
discover  between  these  two  jnoments  ?  (The  product  of  a  force 
by  the  lever  arm  on  which  it  acts  is  called  the  "moment"  of 
the  force.) 

(b)  Change  one  of  the  weights  and  again  compare  the 
moments. 

(e)  Hang  two  weights,  say  a  100-g.  weight  1J\  and  a  50-g. 
weight  JF2,  at  different  points  on  the  left  side  of  the  fulcrum 
and  not  too  close  to  it,  and  then  balance  the  lever  by  hanging  a 
200-g.  weight  JF3  at  the  proper  point  on  the  other  side.  Com- 
pare the  sum  of  the  moments  of  the  first  two  forces  with  the 
moment  of  the  second. 


THE  PBINCIPLE  OF  MOMENTS 


45 


(d )  Hang  some  unknown  weight  X  from  a  point  near  the  left 
end  at  a  distance  I  from  the  fulcrum,  and  balance  it  by  a  known 
weight  W  hung  at  the  proper  point  on  the  other  side.     By  apply- 
ing the  principle  of  moments,  which  you  learned  in  (a),  (6),  and 
(c),  find  the  value  of  X.    Weigh  it  on  the  balance  and  compare 
the  two  results. 

(e)  Hang  from  different  points  on  the  right  side  an  unknown 
weight  X  and  a  known  weight  Wv  and  balance  by  two  known 
weights   Jr3  and  JF4  placed   at  different  points  on  the   other 
side.   Let  I  represent  the  distance  of  X  from  the  fulcrum.   Com- 
pute the  weight  of  the  unknown  body  and  compare  with  the 
result  of  a  direct  weighing. 

(/)  Slip  the  knife-edge  C  to  some  point  0  and  clamp.  Slip 
a  known  weight,  say  200  g.,  along  between  0  and  B  until  the 
beam  rests  horizontally  when  placed  in  the  support.  Then  by 
applying  the  principle  of  moments  find  the  weight  of  the  beam 
on  the  assumption  that  the  whole  effect  of  the  earth's  attrac- 
tion on  the  beam  is  equivalent  to  one  single  force  equal  to  the 
whole  weight  of  the  beam  and  applied  at  the  first  position  of 
the  knife-edge,  i.e.  at  (7,  the  center  of  gravity  of  the  beam. 

If  W  represents  the  weight  of  the  beam,  the  principle  of 
moments  then  gives: 

W  X  distance  CO  =  known  weight  X  its  distance  from  O. 

Compare  the  result  with  a  direct  weighing  of  the  beam. 

Tabulate  as  follows : 

(«)  wi  =- 


its  lever  arm  =  

its  moment  =  ~|     per  cent  of 

its  lever  arm  =  

its  moment  =  )  '    error=  — 

its  lever  arm  =  

its  moment-  =  \    per  cent  of 

its  lever  arm  =  

its  moment  =  J  '    error  =  — 

its  lever  arm  =  

its  moment  =•  "1 
f-  ;  sum    =  

its  lever  arm  =  

its  moment  —  J 

its  lever  arm  =  

its  moment  =  .  1  per  cent  of 

its  lever  arm  =  

L    error  =  — 
its  moment  =  . 

.    Y                 —.  

by  direct  weighing  A' 

46  LABORATORY  PHYSICS 

(e)   W3  = ;  its  lever  arm  = ;  its  moment  =  — 

W4  = ;  its  lever  arm  — ;  its  moment  =  — 

Wl  = ;  its  lever  arm  = ;  its  moment  = . 

/      = ;  .-.  X                 = ;  by  direct  weighing  A'  — . 

(/)  Reading  of  knife-edge  atC  = ;  reading  at  O  

.-.  Lever  arm  OC  = ;  known  weight      — ;  its  lever  arm      = 

.;.  Weight  of  bar  = ;  by  direct  weighing  = ;  per  cent  of  error  = . 

State  what  general  conclusion  you  are  able  to  draw  from  (a), 
(5),  and  (<?).  State  what  method  the  experiments  have  shown 
you  for  finding  the  weight  of  any  body  without  the  aid  of  a 
pair  of  scales.  Where  does  the  result  of  (/)  show  that  the  total 
weight  of  a  body,  i.e.  the  sum  of  the  forces  of  gravity  which  act 
upon  its  particles,  may  be  considered  as  concentrated  ? 


EXPERIMENT  16 

THE  PRINCIPLE  OF  WORK  IN  THE  CASE  OF  THE  INCLINED 
PLANE 

Since  the  work  which  a  force  accomplishes  is  equal  to  the 
product  of  the  force  by  the  distance  through  which  it  moves 
the  point  upon  which  it  acts,  the  work  done  by  a  force  F 
(Fig.  28)  in  moving  a  mass  a  distance  I  (=  on)  up  the  inclined 
plane  on  is  equal  to  Fl.  But  the  work  done  against  gravity  is 
equal  to  the  product  of  the  weight  W  which  is  moved  times 
the  vertical  height  h  (=  mri)  through  which  W  has  been  raised. 

The  object  of  this  experiment  is  to  find  what  relation  exists 
between  the  work  Fl  of  the  acting  force  and  the  work  Wh  of 
the  resisting  force,  in  case  there  is  no  friction. 

Set  the  inclined  plane  of  Fig.  28  at  an  angle  of  about  45°; 
hang  a  convenient  weight,  say  200  g.,  at  F,  and  by  means  of 
nails  or  shot  adjust  the  weight  of  the  carriage  and  contents 
till  it  remains  in  place  on  the  table. 


THE  LAW  OF  THE  INCLINED  PLANE 


47 


Add  nails  or  shot  to  the  carriage  until  with  continued  slight 
tapping  on  the  plane  the  carriage  will  just  move  slowly  and 
uniformly  down. 

Remove  nails  one  by  one,  and  lay  them  aside  together,  until, 
with  like  tapping,  the  carriage  moves  uniformly, up. 

Weigh  the  carriage  with  contents  on  the  beam  balance,  and 


FIG.  28 

label  the  weight  "  JFup."  Then  weigh  again  after  the  nails  which 
were  laid  aside  have  been  added,  and  label  this  weight  "  W  down." 

Measure  carefully  with  a  meter  stick  the  height  of  the  plane 
TWW,  and  label  it  h.  Similarly,  measure  the  length  of  the  plane  on 
and  label  it  I. 

Take  the  mean  of  "IF up"  and  "TPdown"  as  the  weight  W 
which  the  force  F  would  support  on  the  plane  if  there  were 
no  friction. 


48  LABORATORY  PHYSICS 

Change  the  angle  which  on  makes   with  the  horizontal  to 
about  30°  and  repeat  all  observations. 

Tabulate  as  follows : 
Trial       F        W  up    W  down      W  h  I  Fl          Wh 


State  in  words  the  law  shown  above  to  exist  between  the 
weight  on  a  plane  and  the  force  which  must  act  parallel  to  the 
plane  to  keep  it  in  place. 

If  the  board  on  were  gradually  tipped  up  so  that  h  became 
larger  and  larger,  would  W,  the  weight  which  could  be  supported 
by  a  given  force  F,  vary  directly  or  inversely  with  h  ?  What 
sort  of  curve  is  the  graphic  representation  of  this  relation  ? 

EXPERIMENT  17 
THE  LAWS  OF   THE   PENDULUM 

I.  To  find  whether  or  not  the  time  of  swing  is  different  for 
different  amplitudes  and  different  weights:  Attach 
with  sealing  wax  a  small  weight,  preferably  a  steel 
ball  about  3/4  in.  in  diameter,  to  a  fine  thread  about 
180  cm.  long,  and  suspend  it  in  a  wooden  clamp 
with  square  jaws,  like  that  shown  in  Fig.  29. 

Let  one  student  set  his  eye  in  some  particular 
position,  such  that  the  thread  is  in  line  with  some 
fixed  mark  or  small  object.    Then  let  the  pendu- 
lum be  set  into  vibration  through  an  arc  10  cm.  or 
12  cm.  long.    Let  a  second  student  keep  his  eye  on 
the  second  hand  of  a  watch  while  the  first  taps  with 
o      his  pencil  upon  the  table  at  the  instant  of  each 
F|G-  29        passage  of  the   pendulum   past  the  fixed  mark. 
When  the  timekeeper  is  ready  let  him  call  "now"  at  the  instant 


THE  LAWS  OF  THE  PENDULUM  49 

of  some  tap,  and  record  the  hour,  minute,  and  second  at  which 
he  called  it,  and  let  the  other  observer  take  up  the  count  "  one  " 
at  the  instant  of  the  next  tap,  and  continue  up  to  100.  Let  the 
timekeeper  record  again  the  hour,  minute,  second,  and,  if  pos- 
sible, the  fraction  of  a  second,  at  which  the  count  100  occurs. 

Increase  the  amplitude  of  swing  from  20  cm.  to  30  cm.  and 
again  observe  the  time  of  one  hundred  vibrations  exactly  as 
before.  Make  another  trial  when  the  amplitude  has  been  in- 
creased to  2  m.  or  more. 

Suspend  another  pendulum  of  the  same  length  from  support 
to  center  of  bob,  but  of  quite  different  mass  and  material ;  for 
example,  use  for  the  bob  a  lead  bullet,  and  see  whether  one 
pendulum  gains  at  all  upon  the  other  when  they  are  set  going 
together  through  an  arc  of  30  cm.  or  40  cm. 

Tabulate  your  results  as  follows  : 


Arc  10  cm. 

Time  of  begin- 
ning count 

Time  of  ending 
count 

Total           Time  of 
time       one  vibration 

First  trial 

10" 

45m 

10.4* 

10h 

47" 

'  25.0« 

134.68 

1.346« 

Second  trial 

10 

49 

15.0 

10 

51 

29.4 

134.4 

1.344 

Third  trial 

10 

53 

47.2 

10 

56 

2.0 

134.8 

1.348 

Mean     = 



Arc  SO  cm. 
First  trial 
Second  trial 

Mean     =      

Arc  200  cm. 

First  trial 

So  long  as  the  amplitude  is  small,  do  you  find  that  the  period 
depends  upon  it  at  all?  What  is  the  effect  of  a  very  large 
amplitude?  What  influence  has  the  weight  of  the  bob  upon 
the  period  of  a  pendulum  ? 

II.  To  find  the  relation  between  the  lengths  of  two  pendulums 
and  their  periods.  Replace  the  last  pendulum  by  a  second  one 
which  has  a  bob  like  the  first,  and  adjust  its  length  by  slipping 


50  LABORATORY  PHYSICS 

it  through  the  clamp,  the  screw  being  only  moderately  tight, 
until  it  makes  exactly  two  swings  to  every  one  made  by  the 
pendulum  180  cm.  long.  In  order  to  make  this  adjustment,  let 
one  student  tap  the  floor  at  the  instant  of  each  passage  of  the 
long  pendulum  through  its  middle  position,  while  another  does 
the  same  with  the  short  one.  Adjust  until  the  taps  coincide. 

Measure  the  lengths  of  the  two  pendulums  from  the  bottom 
of  the  clamp  to  the  top  of  the  ball,  and  add  to  each  measure- 
ment the  radius  of  the  ball.  From  these  results  predict,  if 
you  can,  how  long  a  pendulum  must  be  made  to  vibrate  three 
times  as  fast  as  the  180-cm.  pendulum.  Test  your  conclusions 
experimentally.  Record  thus : 

Length  of  pendulum  No.  1  =  — 
Length  of  pendulum  No.  2  =  — 
Length  of  pendulum  No.  3  =  — 
Length  No.  1  _  /Period  No.  1 

Length  No.  2  ~  (^Period  No.  2 

Length  No.  1  _  /Period  No.  1\2_  ,( 

Length  No.  3  ~  (^Period  No.  3/  ~ 

III.  To  find  from  the  above  data  the  length  of  the  second 
pendulum.  Take  a  mean  of  all  the  above  observations  with 
shorter  arcs  on  the  time  of  one  vibration  of  the  longest  pendulum. 
From  this  mean  and  the  measured  length  of  this  pendulum  com- 
pute, with  the  aid  of  the  law  just  found  connecting  lengths  and 
periods,  the  length  of  a  pendulum  which  will  beat  seconds. 

In  order  to  obtain  this  quantity  as  accurately  as  possible, 
determine  it  again  from  the  above  data  by  the  graphical  method 
as  follows.  Let  ^,  #2,  t3  be  the  respective  periods  of  the  three 
pendulums,  and  lv  /2,  13  the  corresponding  lengths.  Thus,  in 
the  example  given  above, 

tl  =  1.346  sec.       /2  =  \  x  1.346  =  .673  sec.        ta  =  -J  x  1.346  =  .4487  sec. 
<,2  =  1.812  sec.       /"«  =  .4530  sec.       /!,«  =  .2013  sec. 

/,  =  180.00  cm.     I,  =  45.00  cm.       /.,  =  20.00  cm. 


THE  LAWS  OF  THE  PENDULUM 


51 


Now  plot  £j2,  £22,  £32  as  distances  to  the  right  of  O  Y  (Fig.  30), 
and  lv  lz,  13  as  distances  above  OX,  using  a  scale  large  enough 
to  make  the  figure  cover  a  full  page  and  thus  obtain  three 
points  1,  2,  3.  With  a  pencil  having  a  very  fine  point  draw  the 
straight  line  through  0,  which  passes  as  near  as  possible  to  all 
of  the  points  1,  2,  3.  Read  off  upon  this  straight  line  the  length 


.5      .6     .7      .8      .9       1.0     1.1     1.2      1.3      14     1.5     1.6     II 

(Periods  of  vibration  in  seconds)2 
FIG.  30 

I  corresponding  to  the  value  ft  =  1.  This  is  the  length  of  the 
seconds  pendulum. 

This  graphical  method  here  outlined  is  often  the  simplest  and 
most  satisfactory  way  of  averaging  a  number  of  observations. 

State  in  your  own  words  the  laws  of  the  pendulum  which 
have  been  proved  by  the  above  experiments. 

How  would  you  obtain  from  the  graph  the  time  of  a  pendu- 
lum of  any  assigned  length,  say  141  cm.  ? 

It  is  shown  in  more  advanced  work  in  physics  that  the  velocity 
g  which  a  falling  body  acquires  in  a  second  can  be  found  by  mul- 
tiplying the  length  of  the  seconds  pendulum  by  7r2.  Compute 
g  in  this  way  and  compare  with  the  accepted  value,  viz.  980. 


52  LABORATORY  PHYSICS 

EXPERIMENT  18 

THE  LAW  OF  MIXTURES  AND  THE  WATER  EQUIVALENT 
OF  A  METAL  VESSEL 

I.  The  law  of  mixtures.  The  unit  of  heat  is  called  the 
calorie.  It  is  defined  as  the  amount  of  heat  which  passes  into 
1  g.  of  water  when  its  temperature  rises  1°  C.,  or  the  amount 
which  passes  out  of  1  g.  of  water  when  its  temperature  falls 
1°  C.  Thus,  when  the  temperature  of  100  g.  of  water 
rises  10° C.,  we  say  that  100  x  10  =  1000  calories 
of  heat  have  entered  the  water ;  or  when  the  tem- 
perature of  100  g.  of  water  falls  5°  C.,  we  say 
that  500  calories  of  heat  have  passed  out  of  the 

FIG.  31          Water' 

Allow  a  dry  thermometer  to  stand  for  two  or 

three  minutes  in  a  metal  vessel  of  at  least  300  cc.  capacity,— 
for  example,  the  inner  vessel  i  of  the  calorimeter  of  Fig.  31,  and 
then  take  its  reading  and  call  this  the  temperature  of  the  room. 
(a)  From  a  vessel  of  cold  water  pour  100  g.  of  water  into  each 
of  two  small  vessels,  —  for  example,  the  small  brass  cylinders  used 
in  Experiment  3.  By  heating  with  a  Bunsen  flame  and  by  con- 
tinual stirring  adjust  the  temperatures  of  the  two  vessels  of  water 
until  one  is  6°  or  8°  below  the  temperature  of  the  room  as  meas- 
ured by  one  thermometer,  while  the  other  is  about  the  same 
amount  above  it  as  measured  by  a  second  thermometer.  Imme- 
diately after  taking  these  temperatures  pour  the  two  bodies  of 
water  together  into  the  vessel  which  is  at  the  temperature  of 
the  room.  Stir  for  about  one  minute  with  both  thermometers, 
then  take  the  temperature  of  the  mixture  on  each  thermometer.1 

1  Use  two  thermometers  because  the  temperature  of  one  vessel  would  other- 
wise change  while  that  of  the  other  was  being  taken.  Take  the  final  temperature 
with  both  thermometers  because  the  readings  of  inexpensive  thermometers  often 
differ  from  one  another  as  much  as  £°  C. 


THE  LAW  OF  MIXTURES  53 

Compute  and  record  how  many  calories  of  heat  the  warmer  water 
has  lost  and  how  many  the  colder  water  has  gained. 

(b)  Repeat,  this  time  mixing  200  g.  at  a  temperature  about 
6°  C.  below  that  of  the  room  with  100  g.  at  a  temperature  12°  C. 
above  that  of  the  room.  Record  thus : 

(a) 

Temperature  of  room  =  19.15°C. 

Temperature  of  first  100  g.  water  =  12.7°  C. 

Temperature  of  second  100  g.  water  =  25.7°  C. 

Final  temperature  of  mixture  on  first  thermometer      =  19.1°C. 
Final  temperature  of  mixture  on  second  thermometer  =  19.3°  C. 
Number  of  calories  gained  by  first  100  g. 
Xumber  of  calories  lost  by  second  100  g. 

(b) 
Temperature  of  200  g.  water  =  °  C. 

Temperature  of  100  g.  water  =  °  C. 

Final  temperature  of  mixture  on  first  thermometer       =  °C. 

Final  temperature  of  mixture  on  second  thermometer  =  °C. 

Number  of  calories  gained  by  the  200  g. 
Number  of  calories  lost  by  the  100  g. 

State  in  your  notebook  the  relation  which  you  find  to  hold  in 
the  above  experiments  between  the  number  of  calories  gained  by 
the  body  whose  temperature  rises  and  the  number  lost  by  the  body 
whose  temperature  falls,  remembering,  of  course,  that  your  tem- 
perature readings  may  easily  be  in  error  as  much  at  .1°.  This 
is  found  to  be  a  law  which  governs  the  process  of  heat  exchange 
in  all  cases  of  mixture  of  bodies  at  different  temperatures. 

In  the  above  experiments  the  vessel  into  which  the  water 
was  finally  poured  was  in  every  case  at  the  temperature  of  the 
room.  The  next  experiment  is  one  in  which  this  is  not  the  case. 

II.  Water  equivalent  of  a  metal  vessel.  Pour  150  g.  of  water 
into  the  inner  vessel  i  (Fig.  31)  of  the  calorimeter1  and  100  g. 

1  If  a  calorimeter  is  not  available,  use  two  of  the  small  cylinders  of  Experiment 
3,  but  in  this  case  put  75  g.  of  water  into  each  and  make  the  temperature  of  one 
about  as  far  above  the  temperature  of  the  room  as  that  of  the  other  is  below  it. 


54  LABORATORY  PHYSICS 

into  one  of  the  small  cylinders  used  in  Experiment  3.  Adjust 
the  temperature  of  the  150  g.  until  it  is  about  10°  below  that 
of  the  room,  while  the  temperature  of  the  100  g.  is  made  a  little 
more  than  one  and  a  half  times  as  much  above  that  of  the  room. 
Place  the  inner  vessel  of  the  calorimeter  in  the  outer  one  o 
(Fig.  31),  supporting  it  by  the  ring  r.  This  is  done  to  avoid  com- 
municating heat  to  the  water  from  the  hand.  With  different  ther- 
mometers, stir  the  water  in  each  vessel  thoroughly,  and  at  the 
same  time  tip  the  vessel  containing  the  cold  water  so  as  to  bring 
the  water  into  contact  with  as  much  of  the  walls  as  possible. 
This  is  to  give  the  whole  of  the  vessel  the  temperature  of  the 
water.  Read  the  temperature  of  the  water  in  each  vessel  very 
accurately,  then  quickly  pour  the  warmer  water  into  the  colder. 
Stir  for  half  a  minute,  then  read  the  final  temperature  on  each 
thermometer.  Compute  the  number  of  calories  lost  by  the  hot 
water  and  the  number  gained  by  the  cold.  They  are  no  longer 
equal.  Why  ?  From  the  difference  and  the  number  of  degrees 
through  which  the  vessel  has  been  raised,  find  the  number  of 
calories  required  to  raise  it  through  1°  C.  This  is  called  the  water 
equivalent  of  the  calorimeter,  since  it  is  the  number  of  grams  of 
water  to  which  the  vessel  is  thermally  equivalent.  The  follow- 
ing are  typical  observations. 

Temperature  of  the  150  g.  =  8.1°  C. 

Temperature  of  the  100  g.  =  38.0°  C. 

Temperature  of  mixture  =  19. 5°  C. 

Rise  in  temperature  of  vessel  =  11.4°C. 

Calories  gained  by  cold  water  =  1710 

Calories  lost  by  hot  water  =  1850 

Difference  (=  calories  going  to  vessel)  =     140 

Water  equivalent  of  vessel  =   12.3 

The  calculated  value  of  the  water  equivalent  of  a  brass  vessel  is  its 
weight  (in  this  case  135  g.)  times  the  specific  heat  of  brass  (viz.  .095;  see 
Experiment  19).  This  product  is  in  this  case  equal  to  12.8,  and  differs  from 
the  observed  value,  12.3,  by  4  per  cent. 


SPECIFIC  HEAT 


55 


The  only  reason  for  making  the  initial  temperature  of  the 
100  g.  one  and  a  half  times  as  far  above  the  temperature  of  the 
room  as  that  of  the  150  g.  was  below  it  was  to  make  the  final 
temperature  of  the  mixture  the  same  as  that  of  the  room.  Can 
you  see  why  this  arrangement  is  desirable  if  we  wish  to  know 
the  temperature  of  the  mixture  accurately  ? 

Why  did  we  not  need  to  consider  the  heat  absorbed  by  the 
vessel  into  which  we  poured  the  two  bodies  of  water  in  the 
experiments  on  the  law  of  mixtures? 

If  you  read  one  of  the  thermometers  which  gave  you  the 
final  temperature  of  the  mixture  .1°  too  high,  what  is  the  real 
value  of  the  water  equivalent?  (Actually  work  it  out,  making 
the  final  temperature  .1°  higher.)  Do  you  then  consider  that 
your  result  is  within  the  limits  of  legitimate  observational  error? 


EXPERIMENT  19 
SPECIFIC   HEAT 

I.  Relative  amounts  of  heat  given  up  by  equal  weights  of 
lead,  iron,  and  aluminum  in  falling  i°C.1  Let  the  tops  be  un- 
screwed from  three  steam  boilers  such  as  those  shown  in  Fig.  36, 
and  let  each  boiler  be  filled  with  enough  water 
to  stand  say  half  an  inch  high  in  the  gauge 
shown  on  the  right.  Let  Bunsen  burners  be 
lighted  under  each ;  then  let  one  student  weigh 
out  150  g.  of  lead  shot,  place  it  in  the  dipper  d 
(Fig.  32),  and  set  the  latter  inside  the  boiler. 
Let  another  do  the  same  with  150  g.  of  small  F]f,  32 

iron  nails,  and  a  third  with  150  g.  of  aluminum 
punchings.  Let  each  weigh  or  measure  out  150  g.  of  water,  place 

1  It  is  intended  that  either  three  or  six  students  work  together  on  this  experi- 
ment, according  as  the  class  has  been  working  singly  or  in  groups  of  two. 


56  LABORATORY  PHYSICS 

it  in  one  of  the  cylinders  used  in  Experiment  3,  and  bring  it  to 
the  temperature  of  the  room.  Let  each  student  take  and  record 
the  temperature  of  the  water  in  each  of  the  three  cylinders. 

After  the  water  has  been  boiling  for  about  five  minutes  in 
each  boiler,  let  each  student  quickly  pour  the  contents  of  his 
dipper  into  the  water  in  his  cylinder;  then  let  him  stir  the 
mixture  for  at  least  half  a  minute  and  take  the  final  tem- 
perature in  each  of  the  three  vessels.  (At  this  point  let  each 
student,  in  preparation  for  II,  fill  his  dipper  with  dry  shot  until 
dipper  and  shot  weigh  between  800  g.  and  900  g.;  then  let  him 
take  the  weight  exactly,  place  in  the  boiler,  and  sink  his  ther- 
mometer in  the  shot  so  that  the  bulb  is  well  down  toward  the 
bottom.)  Since,  in  the  above  experiment,  equal  weights  of  the 
three  metals  have  been  raised  to  the  same  temperature  and  then 
plunged  into  equal  quantities  of  water  at  the  same  tempera- 
ture, if  the  final  temperatures  are  different,  what  conclusion 
must  you  draw  regarding  the  capacities  for  giving  out  heat 
which  equal  weights  of  different  bodies  have  per  degree  fall  in 
their  temperatures? 

The  number  of  calories  of  heat  required  to  raise  the  temperature 
of  1  g.  of  a  substance  1°  C.,  or  the  number  of  calories  given  out  by 
1  g.  in  cooling  1°  (7.,  is  called  the  specific  heat  of  the  substance. 

Record  in  your  notebook  what,  in  a  general  way,  your  experi- 
ment shows  about  the  relative  specific  heats  of  different  metals, 
and  about  how  many  times  it  shows  the  specific  heat  of  aluminum 
to  be  greater  than  that  of  iron,  and  that  of  iron  to  be  greater 
than  that  of  lead.  (These  specific  heats  must  be  approximately 
proportional  to  the  three  temperature  changes,  since  each  metal 
has  fallen  through  approximately  the  same  number  of  degrees, 
i.e.  from  about  100°  to  about  the  temperature  of  the  room.) 

II.  Accurate  determination  of  the  specific  heat  of  lead.  Weigh 
the  inner  vessel  i  of  the  calorimeter  of  Fig.  31 ;  then  prepare 
some  water  whose  temperature  is  about  12°  C.  below  that  of 


SPECIFIC  HEAT  57 

the  room.  Pour  about  200  g.  of  it  into  the  calorimeter.  Weigh 
again,  and  replace  the  calorimeter  in  its  jacket  o  (Fig.  31).1 

With  a  glass  rod  or  a  pencil  stir  the  shot  in  the  dipper,  and 
after  it  has  been  heating  for  fifteen  minutes  or  more  record  the 
temperature  indicated  by  the  thermometer  immersed  in  it. 

Transfer  the  thermometer  to  the  cold  water  in  the  calorimeter 
and  stir  thoroughly.  When  its  temperature  reaches  some  con- 
venient point,  which  should  not  be  less  than  8°  C.  below  the 
temperature  of  the  room,  quickly  pour  the  shot  from  the  dipper 
into  the  water.  (If  dew  has  collected  on  the  outside  of  the 
inner  vessel,  wipe  it  all  off  just  before  mixing.) 

Stir  the  mixture  for  about  two  minutes,  then  take  the  final 
temperature.  Weigh  the  dipper,  then  tabulate  results  as  follows: 

Weight  of  dipper  +  shot  =  1201  g. 

Weight  of  dipper  alone  =  103  g. 

.-.  Weight  of  shot  alone  =  1098  g. 

Weight  of  calorimeter  =  157  g. 

Weight  of  calorimeter  +  water  =  415.9  g. 

.-.-Weight  of  water  alone  =  258.9  g. 

Temperature  of  room  =  22°  C. 

Temperature  of  shot  =  98.5°  C. 

Initial  temperature  of  water  =  12. 8°  C. 

Final  temperature  of  mixture  =  22.3°  C. 

Rise  in  temperature  of  water  =  9.5°C. 

Water  equivalent  of  calorimeter,  from  Experiment  18  =  14.7  g. 

Weight  of  water  +  water  equivalent  =  273.6  g. 

Number  of  calories  absorbed  by  water  +  calorimeter  =  2599 

Fall  in  temperature  of  shot  •  =  76.2°  C. 

.-.Heat  given  up  by  shot  per  gram  per  1°C.  =  specific 

heat  of  lead  =  .0311 

Accepted  value  =  .0315 

Per  cent  of  error  =1.3 

1  If  the  laboratory  is  not  equipped  with  calorimeters,  use  instead  the  cylinder 
of  Part  I  without  any  jacket.  In  this  case  make  the  weights  of  water  in  the 
cylinder  and  of  lead  in  the  dipper  one  half  of  the  above  amounts. 


58  LABORATORY  PHYSICS 

State  in  your  notebook  what  you  understand  to  be  represented 
by  the  quantity  which  you  have  found.1 

When  the  shot  and  the  water  were  mixed  the  changes  in  the 
temperature  of  each  took  place  very  rapidly  at  first,  but  very 
slowly  as  the  temperature  of  each  approached  the  final  value. 
Can  you  see  a  reason,  therefore,  why  it  was  advisable  to  choose 
the  conditions  so  that  the  final  temperature  should  be  close  to 
the  temperature  of  the  room?  Remember  in  your  answer  that 
it  was  necessary  to  wait  two  or  three  minutes  for  the  mixture 
to  reach  its  final  temperature,  and  that  a  body  which  is  hotter 
than  the  room  is  always  losing  heat  to  the  room,  while  one 
which  is  colder  than  the  room  is  always  gaining  heat  from  it. 
It  is  these  losses  of  heat  by  radiation  which  constitute  the 
greatest  difficulty  in  the  way  of  accurate  measurements  by  the 
method  of  mixtures. 

1  A  further  very  interesting  experiment  which  may  be  inserted  for  the  benefit 
of  those  who  have  time  and  inclination  for  extra  work  is  the  following. 

To  find  the  temperature  of  a  white-hot  body.  By  means  of  a  thin  copper  wire 
suspend  from  a  support  placed  from  50  cm.  to  100  cm.  above  the  table  a  piece 
of  copper  rod  about  2  cm.  long  and  12  mm.  in  diameter.  Adjust  the  length  of 
the  suspension  so  that  the  copper  hangs  in  the  hottest  part  of  a  Bunsen  flame 
(just  above  the  inner  cone). 

Weigh  a  calorimeter  of  300  cc.  capacity  ;  then  fill  it  about  half  full  of  water 
whose  temperature  has  been  reduced  12°  or  15°  below  that  of  the  room,  and 
weigh  again.  Then  replace  it  in  its  jacket. 

After  the  copper  has  been  heating  for  about  ten  minutes  take  the  temperature 
of  the  water  very  carefully  (it  should  now  be  from  8°  to  10°  below  the  tempera- 
ture of  the  room) ;  then,  all  in  the  same  second,  remove  the  flame  and  lift  the 
calorimeter  so  as  to  bring  the  white-hot  copper  to  the  bottom  of  the  vessel  of  water. 

Stir  the  water, thoroughly  for  one  or  two  minutes;  then  take  the  final 
temperature. 

Weigh  the  copper  rod  and  with  it  as  much  of  the  copper  wire  as  was 
immersed. 

Assuming  that  .095  calories  (the  specific  heat  of  copper)  came  out  of  each 
gram  of  copper  for  each  degree  of  fall  in  its  temperature,  calculate  what  was 
the  temperature  of  the  white-hot  copper. 

Duplicate  conditions  as  nearly  as  possible  and  see  how  closely  two  observa- 
tions will  agree. 


THE  MECHANICAL  EQUIVALENT  OF  HEAT        59 

Why  was  it  unnecessary  to  attempt  to  weigh  the  shot  to 
tenths  of  a  gram? 

After  the  experiment  spread  out  the  shot  in  a  thin  layer  on 
a  cloth  to  dry. 


EXPERIMENT  20 

THE  MECHANICAL   EQUIVALENT  OF    HEAT 

The  object  of  this  experiment  is  to  show  that  when  a  falling 
body  strikes  the  earth  the  kinetic  energy  of  the  moving  mass 
is  transformed  into  the  energy 
of  molecular  vibrations,  i.e.  into 
heat,  and  to  find  how  many  gram 
meters  of  mechanical  energy 
must  disappear  in  order  to  pro- 
duce 1  calorie  of  heat.  This 
quantity  is  called  the  "  mechan- 
ical equivalent  of  heat."  It  is 
obtained  by  finding  the  rise  in 
the  temperature  of  shot  when  it 
falls  through  a  known  height. 

Pour  about  2  kg.  of  dry  shot 
into  a  metal  vessel  and  set  it 

in  a  cool  place,  e.g.  in  a  bath  of  ice  water,  until  its  temperature 
is  5°  or  6°  below  that  of  the  room. 

Pour  this  shot  into  a  paper  tube  (Fig.  33)  about  a  meter  long 
and  5  cm.  or  6  cm.  in  diameter,  made  by  rolling  up  a  large  num- 
ber of  turns  of  heavy  brown  paper  and  then  securing  them  with 
glue  and  string.  The  tube  should  be  closed  with  two  tightly 
fitting  corks. 

Mix  the  shot  very  thoroughly  by  shaking  the  tube,  and  by 
slowly  inclining  it  so  that  the  shot  will  run  from  end  to  end. 


FIG.  33 


60  LABORATORY  PHYSICS 

In  so  doing,  however,  grasp  the  tube  near  the  middle  rather 
than  at  the  ends,  for  it  is  desirable  that  the  temperature  of  the 
ends  be  not  influenced  by  the  heat  of  the  hands. 

After  inverting  in  this  way  from  five  to  ten  times,  remove 
the  upper  cork  A  and  insert  cork  C  (Fig.  33),  through  which 
passes  a  thermometer;  then  gradually  incline  the  tube  until 
all  the  shot  has  run  down  to  the  thermometer  end  and  there 
completely  surrounds  the  bulb. 

Holding  the  tube  inclined  as  in  the  figure,  twist  the  thermom- 
eter about  in  the  shot  for  about  two  minutes,  and  then  take  the 
temperature.  If  this  is  more  than  2°  or  3°  below  the  tempera- 
ture of  the  room,  continue  the  shaking  and  rolling  of  the  shot 
from  one  end  to  the  other  until  its  temperature  has  risen  to 
within  about  3°  C.  of  that  of  the  room. 

Record  this  temperature,  quickly  replace  cork  C  by  cork  J,  hold 
the  tube  upright  as  in  the  figure,  and  turn  it  completely  over 
say  seventy  times  in  rapid  succession,  placing  the  lower  end  on 
the  table  at  each  reversal,  so  that  the  falling  shot  may  not  force 
out  the  corks.  At  each  reversal  the  potential  energy  acquired 
by  the  shot  in  being  lifted  the  length  of  the  tube  is  converted 
into  kinetic  energy  in  the  descent,  and  this  kinetic  energy  is 
all  transformed  into  heat  energy  at  the  bottom.  On  account  of 
the  poor  conductivity  of  the  cork  and  paper  practically  all  of 
this  heat  goes  into  the  shot,  and  but  an  insignificant  portion 
of  it  into  the  corks  and  tube. 

After  the  seventy  reversals  very  quickly  replace  cork  A  by 
cork  (7,  and  take  as  before  the  final  temperature  of  the  shot. 

Remove  cork  (7,  set  the  tube  on  end,  and  measure  the  distance 
from  the  top  of  the  shot  to  the  position  which  was  occupied  by 
the  bottom  of  cork  A.  This  is  the  mean  height  through  which 
the  shot  has  fallen  at  each  reversal. 

The  total  quantity  of  work  which  has  been  transformed 
into  heat  is  the  weight  IF  of  the  shot  X  the  height  //  of  fall 


THE  MECHANICAL  EQUIVALENT  OF  HEAT         61 

(expressed  in  meters)  x  70.  The  number  of  calories  of  heat 
developed  is  the  weight  of  the  shot  W  x  its  specific  heat 
(.0315)  x  the  rise  in  temperature  (£2  —  tj.  Hence,  if  J  represent 
the  number  of  gram  meters  of  energy  in  a  calorie,  we  have 

J-  W  x  (*2  -  tj)  X  .0315  =  70  -  W  •  h. 
70  h 


- 


-*!>  .0815 


It  will  be  noticed  that  the  weight  W  of  the  shot  cancels  out  ; 
hence  it  need  not  be  taken. 

In  the  above  directions  the  attempt  is  made  to  eliminate 
radiation  and  conduction  losses  by  making  the  initial  tempera- 
ture of  the  shot  about  as  far  below  the  temperature  of  the  room 
as  the  final  temperature  is  to  be  above  it.  This  is  the  usual 
way  of  eliminating  radiation,  when,  as  in  this  case,  the  change 
in  temperature  between  the  readings  of  the  initial  and  final 
temperatures  takes  place  rapidly  and  at  a  uniform  rate. 

Repeat  the  experiment  several  times  if  time  permits.  Record 
the  results  thus  : 


First 

Second 

Third 

trial 

trial 

trial 

Temperature  of  room 

=    18.5°C. 

18.5°  C. 

18.5°C. 

Mean  value 

Initial  temperature 

=     16.0°  C. 

17.1°C. 

16.7°  C. 

=  437  g.  m. 

Final  temperature 

=    21.7°C. 

22.  6°  C. 

21.0°C. 

Accepted  value 

Number  of  reversals 

=  100 

100 

80 

=  427  g.  m. 

Height  of  fall  (A) 

.76  rn. 

.70  m. 

.70  m. 

Mechanical  equivalent  =  423  g.  m.     439  g.  m.   449  g.  m.      %  of  error  =  2.4 

What  conclusions  do  you  draw  from  your  experiment? 

The  chief  source  of  error  in  the  experiment  arises  from  the  fact 
that  the  thermometer  requires  considerable  time  to  come  to  the 
temperature  of  the  shot.  During  all  this  time  the  shot  is  gain- 
ing or  losing  heat  by  conduction  and  radiation,  so  that  the 
temperature  indicated  may  not  be  quite  the  mean  temperature 
of  the  shot.  This  source  of  error  is  unavoidable. 


62  LABORATORY  PHYSICS 

Why  did  we  attempt  to  have  the  initial  temperature  as  far 
below  the  temperature  of  the  room  as  the  final  temperature  was 
above  it? 

EXPERIMENT  21 
COOLING  THROUGH  CHANGE  OF  STATE 

I.  Solidification  a  heat-evolving  process.  The  object  of  this 
experiment  is  to  show  that  just  as  it  requires  an  expenditure  of 
heat  energy  to  melt  ice  or  any  other  crystalline  substance,  so 
when  water  or  any  liquid  freezes,  i.e..  changes  back  to  the  crys- 
talline form,  heat  energy  is  given  up  to  the  surroundings. 

Support  vertically  in  a  burette  holder  or  other  clamp  a  test 
tube  in  which  has  been  placed  enough  loose  crystals  of  acetamide 
to  fill  it  about  a  third  full.  Then  heat  gently  with  a  Bunsen 
burner  until  the  crystals  are  all  melted.1  Slowly  insert  a  ther- 
mometer into  the  liquid,  but  watch  the  thread  all  the  time,  and 
if  it  rises  to  within  half  an  inch  of  the  top  of  the  bore,  instantly 
remove  the  bulb  from  the  liquid.  The  thermometer  will  burst 
under  the  force  of  expansion  of  the  mercury  if  the  thread  reaches 
the  top  of  the  bore.  If  there  is  an  expansion  chamber  at  the  top, 
this  danger  is  of  course  avoided.  If  there  is  no  expansion 
chamber,  it  will  be  safer  to  melt  the  acetamide  by  dipping  the 
tube  into  boiling  water  rather  than  by  applying  the  flame  directly. 

As  soon  as  the  liquid  acetamide  has  cooled  down  to  about 
100°  C.,  insert  the  thermometer  in  it  permanently,  and  without 
touching  further  either  the  tube  or  the  thermometer,  watch 
carefully  both  the  liquid  and  the  thread  of  mercury  as  cooling 
takes  place.  The  temperature  may  fall  as  low  as  60°  C.  before 
crystallization  begins.  As  soon  as  crystals  begin  to  form,  what 
sort  of  a  temperature  change  do  you  observe  ?  What  conclusion 
do  you  draw  from  this  observation  ?  Watch  the  temperature  for 
1  If  the  acetamide  has  absorbed  much  moisture,  boil  it. 


COOLING  THROUGH  CHANGE  OF  STATE 


63 


two  or  three  more  minutes  and  decide  whether  or  not  the  temper- 
ature of  a  solidifying  liquid  remains  constant  during  the  process 
of  solidification.  Since  it  is  giving  up  heat  rapidly  all  this  time, 
it  must  get  it  from  some  source.  What  must  this  source  be? 

II.  The  curve  of  cooling.  Again  raise  the  temperature  to  100°C, 
taking  the  precautions  mentioned  above  against  breaking  the 
thermometer.  Record  the  temperature  every  half  minute  as  the 


11-15      17       13      21       23       25       27       29       31       33       35       3?       39      41      «       41 


FIG.  34 

substance  cools  from  about  100°  C.  to  45°  C.  Plot  these  obser- 
vations in  the  manner  shown  in  Fig.  34,  temperatures  being 
represented  by  vertical  distances  and  times  by  horizontal  dis- 
tances. Thus  the  observations  plotted  in  the  figure  began  at 
11:15  A.M.  and  continued  to  11:45  A.M.  The  curve  shows  that 
between  11:15  and  ll:19.5  the  temperature  fell  rapidly  from 
100°  to  71.8°,  that  it  then  rose  suddenly  to  79°,  remained  there 
five  minutes,  then  fell  slowly  during  the  next  twenty  minutes 
from  79°  to  43.5°. 


64  LABORATORY  PHYSICS 

Write  in  your  notebook  a  similar  explanation  of  your  own 
curve.  Almost  any  substance,  if  kept  very  quiet  and  cooled 
through  its  freezing  point,  will  show  the  phenomenon  of  under- 
cooling exhibited  here  by  the  acetamide,  i.e.  its  temperatures 
will  fall  a  little  below  the  freezing  points  before  the  crystalliza- 
tion gets  started.  It  will  then  rise  suddenly  to  the  freezing  point 
and  remain  there  until  the  crystallization  is  practically  complete. 

If  time  permits,  dip  a  test  tube  containing  a  little  distilled 
water  into  a  freezing  mixture  of  salt  water  and  ice,  the  tem- 
perature of  which  is  say  —  8°  C.,  and  see  if  water  too  will  not 
show  the  same  behavior.  (The  tube  must  be  kept  very  quiet.) 
If  you  get  the  temperature  down  to  —  2°  or  —  3°,  lift  the  test 
tube,  stir,  and  observe  the  instant  formation  of  the  crystals  of  ice. 
If  you  wish  to  try  a  substance  which  does  not  undercool,  treat 
a  little  naphthaline  l  precisely  as  you  treated  the  acetamide. 


EXPERIMENT   22 
THE  HEAT  OF  FUSION  OF  ICE 

The  heat  of  fusion  of  ice,  i.e.  the  number  of  calories  of  heat 
required  to  change  a  gram  of  ice  at  0°  C.  into  water  at  0°  C., 
or  the  number  given  up  when  a  gram  of  water  changes  to  ice, 
may  be  determined  experimentally  as  follows. 

Weigh  the  inner  vessel  of  a  calorimeter  of  about  300  cc. 
capacity  first  when  empty,  and  then  after  it  has  been  filled 
about  two  thirds  full  of  water.2 

Heat  this  water  to  a  temperature  of  about  25°  C.  above  that 
of  the  room  ;  then  replace  the  inner  vessel  in  its  jacket  (Fig.  31). 

1  Naphthaline  can  be  obtained  at  any  drug  store.    Acetamide  will  have  to  be 
purchased  at  a  chemical  supply  house. 

2  If  you  use  the  small  cylinders  of  Experiment  3  for  the  calorimeters,  take 
just  half  of  the  amounts  of  ice  and  water  indicated. 


THE  HEAT  OF  FUSION  OF  ICE  65 

Prepare  a  lump  of  clear  ice  of  about  the  size  of  a  hen's  egg, 
and  perform  the  following  operations  in  quick  succession. 

While  one  student  is  drying  the  ice  upon  a  towel  let  another 
stir  the  water  in  the  calorimeter  thoroughly.  If  its  tempera- 
ture is  less  than  15°  C.  above  that  of  the  room,  heat  it  up  again 
until  it  is  between  15°  C.  and  25°  C.  above.  Again  check  the 
weight,  for  the  loss  by  evaporation  may  not  have  been  inappre- 
ciable. Stir  vigorously;  then  quickly  take  a  careful  reading  of 
the  temperature,  keeping  the  thermometer  bulb  all  the  time 
immersed,  and  not  more  than  a  second  or  two  after  the  reading 
let  the  first  student  drop  the  dry  ice  into  the  water,  being  very 
careful  not  to  spill  a  drop.  The  splash  may  often  be  avoided 
by  letting  the  ice  slide  along  the  thermometer  into  the  water. 

Stir  continuously  while  the  ice  is  melting  and  read  the  tem- 
perature of  the  water  just  after  the  ice  has  all  disappeared. 
This  temperature  should  be  from  2°  C.  to!0° C.  below  the  tempera- 
ture of  the  room.  If  it  should  happen  to  be  above  the  room 
temperature,  try  again  \vith  a  slightly  larger  piece  of  ice.  The 
limits  here  given  are  chosen  so  as  to  make  it  legitimate  to 
assume  that  the  heat  exchanges  which  take  place  between  the 
calorimeter  and  the  room  are,  on  the  whole,  negligible. 

Again  weigh  the  inner  vessel  of  the  calorimeter,  with  its 
contained  water,  and  take  the  difference  between  this  weighing 
and  the  last  as  the  weight  of  the  ice. 

Let  x  represent  the  heat  of  fusion  of  ice  and  w  the  weight 
in  grams  of  the  ice  melted.  Then  the  number  of  calories 
expended  in  melting  the  ice  is  ivx.  After  the  ice  is  melted  it 
becomes  iv  grams  of  water  at  0°  C.  This  water  is  then  raised  to 
the  final  temperature  t  of  the  mixture.  The  number  of  calories 
required  for  this  operation  is  wt.  All  of  this  heat  has  come 
from  the  cooling  of  the  water  and  the  calorimeter.  If  the 
weight  of  the  water  cooled  is  W  and  its  initial  temperature  tv 
while  the  water  equivalent  of  the  calorimeter  is  e,  then  the 


66  LABORATORY  PHYSICS 

total  number  of  calories  given  up  by  the  water  and  calorimeter 
is  (W+e)  (ti~t).  Hence,  by  equating  "heat  lost"  and  "heat 
gained,"  it  is  easy  to  obtain  x,  the  only  unknown  quantity  of 
the  equation.  Tabulate  as  follows  : 

Weight  of  calorimeter 

Weight  of  calorimeter  +  water 
.-.  Weight  of  water 

Temperature  of  room 

Initial  temperature  of  water 

Final  temperature  of  water  = 

.-.  Fall  in  temperature  of  water 

Weight  of  calorimeter  +  water  +  ice 
.-.  Weight  of  ice 

Water  equivalent  of  calorimeter  (Experiment  18)  =  — 
.-.  Heat  of  fusion  of  ice 

Accepted  value  is  80. 
.-.  Per  cent  of  error 

State  in  your  notebook  the  meaning  of  the  "  latent  heat  of 
water,"  the  quantity  which  has  been  found  above.1 


EXPERIMENT  23 
THE  BOILING  POINT  OF  ALCOHOL 

The  boiling  point  of  a  liquid  is  denned  as  the  temperature 
at  which  the  pressure  of  its  saturated  vapor  becomes  equal  to 
the  atmospheric  pressure.  There  are,  therefore,  two  ways  in 
which  the  boiling  point  of  alcohol  may  be  obtained,  and  these 

1  A  further  experiment  on  latent  heat,  which  may  be  introduced  for  the 
benefit  of  those  who  have  time  and  inclination  for  extra  work,  is  the  following. 

To  find  the  heat  of  condensation  of  steam.  Pass  dry  steam  into  say  250  g.  of 
cold  water,  the  temperature  of  which  is  10°  C.  below  that  of  the  room,  until  the 
temperature  is  10°  above  that  of  the  room.  Weigh  again  to  find  the  weight  of 
the  steam,  and  then  calculate  as  above  how  many  calories  of  heat  have  been 
given  up  by  each  gram  of  steam  in  condensing. 


THE  BOILING  POINT  OF  ALCOHOL  67 

two  ways  should  give  identical  results.  The  first  is  to  confine 
the  liquid  and  its  vapor  alone  in  a  closed  vessel,  and  then  to  meas- 
ure the  pressure  exerted  by  the  vapor  at  different  temperatures. 
That  temperature  at  which  the  pressure  becomes  equal  to  atmos- 
pheric pressure  will  then  be  the  boiling  temperature.  The  sec- 
ond and  more  direct  way  consists  in  simply  boiling  the  liquid 
in  an  open  vessel  and  observing  the  temperature  indicated  by  a 
thermometer  held  in  the  vapor  rising  from  the  liquid. 

I.  Temperature  at  which  pressure  of  saturated  vapor  becomes 
equal  to  atmospheric  pressure.    A  glass  tube  A  (Fig.  35)  is  closed 
at  one  end,  and  is  then  bent  into  the  U-shape  and  par- 
tially filled  with  mercury.    Some  alcohol  is  then  poured 

in,  which  by  careful  tilting  is  worked  around  into  the 
closed  arm,  while  the  air  is  altogether  worked  out  of 
this  arm.  With  this  arrangement  proceed  as  follows. 

Immerse  the  tube  and  a  thermometer  together  in  a 
vessel  of  water,  and,  keeping  the  short  arm  completely 
immersed,  heat  slowly,  stirring  continually.  As  the  ' 
temperature  increases  a  point  is  reached  at  which  alcohol  vapor 
begins  to  form  in  the  closed  tube.  Still  further  increase  in  tem- 
perature causes  the  mercury  to  sink  farther  and  farther  in  the 
closed  end.  When  the  levels  of  the  mercury  in  the  two  arms 
are  the  same,  it  is  clear  that  the  pressure  of  the  alcohol  vapor 
is  just  equal  to  the  atmospheric  pressure. 

Raise  the  temperature  of  the  water  gradually  and  stir  thor- 
oughly until  this  condition  is  reached ;  then  read  and  record 
the  temperature. 

Continue  heating  until  the  level  in  the  short  arm  is  5  cm. 
lower  than  that  in  the  long  one.  Then  again  read  the  ther- 
mometer and  compute  how  much  the  boiling  point  of  alcohol 
increases  per  centimeter  increase  in  the  barometric  pressure. 

II.  Temperature  of  vapor  rising  from  boiling  liquid.    Place  a 
little  alcohol  in  a  large  test  tube ;  put  a  few  tacks  in  the  bottom 


68  LABORATORY  PHYSICS 

of  the  tube  in  order  to  assure  smooth  boiling;  then  immerse  the 
lower  end  of  the  tube  in  a  vessel  of  water  and  heat  the  water 
until  the  alcohol  boils  vigorously.  Hold  the  bulb  of  a  thermome- 
ter in  the  tube  a  little  distance  above  the  surface  of  the  boiling 
liquid.  As  soon  as  the  thermometer  reading  becomes  station- 
ary, take  the  temperature  and  compare  with  that  obtained  in  I. 
Record  thus : 
I.  Temperature  at  which  alcohol  vapor  exerts  pressure  of  1  atmosphere 

—   0£ 

Temperature  at  which  alcohol  vapor  exerts  pressure  of  1  atmosphere 

+  5 cm.  of  mercury  = ° C. 

Rise  in  boiling  point  of  alcohol  per  cm.  increase  in  pressure  = °C. 

II.  Temperature  of  vapor  rising  from  boiling  alcohol  =  -    — °C. 
Difference  between  results  of  I  and  II  = 

State  in  your  notebook  what  you  consider  to  have  been 
proved  in  this  experiment. 

EXPERIMENT   24 

TO  TEST  THE  FIXED  POINTS  OF  A  THERMOMETER,  AND 
TO  FIND  THE  CHANGE  IN  THE  BOILING  POINT  OF 
WATER  PER  CENTIMETER  CHANGE  IN  THE  BARO- 
METRIC PRESSURE 

Fill  the  boiler  of  Fig.  36  half  full  of  water,  and  thrust  the 
thermometer  through  a  tightly  fitting  cork  in  the  top  until  the 
100°  point  is  only  2  mm.  or  3  mm.  above  the  cork. 

Attach  an  open-arm  manometer  u  (Fig.  36)  to  the  exit  o,  and 
then  boil,  regulating  the  flame  until  the  mercury  stands  at  the 
same  height  in  both  arms  of  the  manometer. 

After  the  water  has  been  boiling  steadily  for  two  or  three 
minutes,  read  the  thermometer  very  carefully.  Then  take  the 
barometer  reading.  Next  place  a  piece  of  tightly  fitting  rubber 
tubing  over  the  escape  tube  e  and  partly  close  the  free  end  of 
it  with  a  pinchcock  until  the  difference  in  the  levels  in  the 


FREEZING  AND  BOILING  POINTS  OF  WATER      69 


FIG.  36 


manometer  arms,  due  to  the  partial  closing  of  the  vent  for  the 
steam,  amounts  to  2  cm.  or  3  cm.  Read  the  thermometer  and 
(with  a  meter  stick)  the  difference  in  the  levels 
in  the  manometer  arms. 

Close  the  pinchcock  still  further,  until  the 
difference  in  level  amounts  to  4  cm.  or  5  cm. ; 
then  read  again. 

Continue  thus,  taking  readings  at  intervals 
of  about  2  cm.,  until  the  difference  in  level 
amounts  to  8  cm.  or  10  cm.  It  may  be  necessary 
to  use  several  burners  in  order  to  obtain  the 
last  readings,  for  the  steam  must  be  generated 
very  rapidly  in  order  to  compensate  for  the 
inevitable  leakage. 

From  each  of  these  readings  calculate  the 
changes  produced  in  the   boiling  point  by  a 
change  of  1  mm.  in  the  barometric  height.    Take  a  mean  of  all 
these  calculations  as  the  correct  value  of  this  quantity. 

From  this  result  and  the  barometer  reading  calculate  what 
your  thermometer  would  read  under  a  pressure  of  76  cm.  The 
error  in  the  graduation  of  the  thermometer  is  the  difference 
between  this  result  and  100. 

Test  the  zero  point  of  the  same  thermometer  by  sinking  it 
up  to  the  zero  mark  in  a  funnel  filled  with  melting  snow  or 
finely  chopped  ice  over  which  a  little  water  has  been  poured, 
and  allowing  it  to  remain  there  until  the  thread  is  stationary. 

Tabulate  results  thus : 

First 

Difference  in  levels  in  gauge 

Corresponding  boiling-point  readings      =  — 

Change  in  boiling  point  per  millimeter  = 

Mean  change  per  millimeter 
.-.  Reading  of  thermometer  at  76  cm.  = 

.-.  Reading  of  thermometer  at  0°  cm.  = 


Second 


Third 


Barometer  height  = 

Error 

Error  = 


70  LABORATORY  PHYSICS 

State  in  your  own  words  the  conclusion  which  you  draw 
from  this  experiment  regarding  the  effect  of  pressure  upon  the 
boiling  point. 


EXPERIMENT   25 
MAGNETIC   FIELDS 

I.  The  magnetic  field  about  a  bar  magnet,  (a)  Lay  a  bar  mag- 
net in  a  groove  in  a  board  (Fig.  37).  Pin  a  sheet  of  blueprint 
paper  over  the  magnet ;  from  a  sifter  containing  iron  filings  sift 
the  filings  evenly,  but  not  too  thickly,  over  the  paper  from  a 
— \  height  of  a  foot  or  two.  Tap 

\.  the   paper  gently  with  a 

—^-^      i  pencil.    The 'filings  will  be 

\.        found  to  have  arranged  thern- 

\    selves  in  lines  running  in 

—    symmetrical  curves  from 
one  pole  around  to  the  other. 

(5)  Hold  a  short  compass  needle  in  a  number  of  positions  over 
the  board,  and  observe  whether  or  not  there  is  any  connection 
between  the  direction  of  the  curved  lines  and  the  direction 
taken  by  the  needle.  These  lines  simply  indicate  the  direction 
of  the  magnetic  force.  They  are  called  magnetic  lines  of  force. 

(c)  Carefully  place  the  board  in  strong  sunlight  without 
jarring  the  filings,  and  wait  until  the  uncovered  parts  of  the 
paper  have  turned  brown.  Return  the  filings  to  the  box  and 
put  the  blueprint  paper  to  soak  in  water  for  about  five  minutes. 
Place  the  paper  flat  against  a  pane  of  glass  to  dry,  and  when 
it  is  dry  fasten  it  in  your  notebook. 

If  blueprint  paper  is  not  provided,  or  if  the  sun  is  not 
bright  enough  to  make  satisfactory  prints,  simply  draw  in  your 
notebook  a  copy  of  the  curves  shown  by  the  filings.  In  these 


MOLECULAR  NATURE  OF  MAGNETISM  71 

drawings  and  also  on  the  blueprints  indicate  the  N  and  S 
poles  of  the  magnets  and  furnish  the  lines  with  arrows  point- 
ing in  the  direction  in  which  an  N  pole  tends  to  move.  (An 
N  pole  is  one  which,  when  the  magnet  is  suspended  freely, 
points  toward  the  north.) 

II.    The  magnetic  fields  about  certain  combinations  of  horse- 
shoe magnets.    By  sprinkling  iron  filings  upon  a  sheet  of  card- 


board or  glass  placed  over  various  combinations  of  magnets,  as 
indicated  in  the  accompanying  figures  (Fig.  38),  determine  the 
nature  of  the  magnetic  field  in  each  case,  and  indicate  by  a 
drawing  in  the  notebook. 

EXPERIMENT  26 
MOLECULAR  NATURE  OF   MAGXETISM 

I.  Making  a  permanent  magnet.  Mark  one  end  of  a  knit- 
ting needle  with  a  file  for  the  sake  of  identification. 

(a)  Stroke  it  once  from  end  to  end  with  the  N  pole  of  a 
horseshoe  or  bar  magnet.  Place  the  needle  on  the  table  in  the 
east-and-west  line  which  passes  through  the  middle  of  a  com- 
pass needle  resting  upon  the  table,  and  slide  the  knitting  needle 
up  toward  the  compass  until  it  produces  in  it  a  deflection  of  10°; 
then  mark  the  positions  of  the  two  ends  of  the  knitting  needle 
on  the  table.  Does  the  near  end  of  the  knitting  needle  repel 
or  attract  the  north-seeking  end  of  the  compass  needle?  Is  it 
an  N  or  an  S  pole?  (If  in  doubt,  suspend  the  needle  in  the 
middle  by  a  thread  and  wire  stirrup  and  see  which  end  points 
north.) 


72  LABORATORY  PHYSICS 

(b)  Reverse  the  knitting  needle  so  that  the  second  end  occu- 
pies exactly  the  position  originally  occupied  by  the  first.    Com- 
pare the  strengths  and  signs  of  the  two  poles. 

(c)  Stroke  the  needle  once  more  with  the  magnet  precisely  as 
at  first,  and  again  bring  it  to  precisely  the  same  position.     Is 
the  deflection  increased?    How  much? 

(d)  Continue  to  stroke  the  magnet  in  the  same  way  until  it 
is  saturated,  i.e.  until  further  stroking  produces  no  more  change 
in  the  effect  upon  the  compass. 

II.  Effect  of  jars  on  a  saturated  magnet,    (a)  -  Drop  the  needle 
on  the  floor  and  again  test  its  strength  exactly  as  before.    Record 
the  change. 

(b)  Strike  the  needle  a  number  of  sharp  blows  against  the 
table  and  test  again. 

(c)  If  magnetization  consists  in  a  particular  arrangement  of 
the  molecules  of  the  needle,  what  effect  would  you  expect  vio-' 
lent  jars  like  the  above  to  have  upon  it? 

III.  Effect  of  breaking  a  magnetized  needle,    (a)  Magnetize  a 
long  darning  needle  and  note  which  end  is  Arand  which  S.    Then 
dip  the  whole  needle  into  a  box  of  iron  filings  and  note  whether 
or  not  it  possesses  any  appreciable  magnetism  in  the  middle. 

(b)  Break  it  in  two  and  test  the  two  freshly  broken  ends  first 
by  means  of  the  compass  and  then  by  means  of  the  iron  filings. 
Test  also  the  old  ends. 

(c)  Break  one  of  the  halves  again  if  possible  and  repeat  as  above. 

(d)  Summarize  the  results  of  these  experiments  and  explain 
the  observed  effects  on  the  assumption  that  a  magnet  consists 
of  rows  of  molecular  magnets  arranged  end  to  end. 

IV.  Effects  of  heating  a  magnet,    (a)  Note  how  much  deflec- 
tion is  produced  when  one  of  the  small  magnets,  say  an  inch 
long,  obtained  by  breaking  the  darning  needle,  is  placed  at  a 
given  distance  from  the  compass ;  then  make  a  stirrup  out  of 
copper  wire,  place  the  needle  in  it,  heat  it  to  redness  in  the 


MOLECULAK  NATURE  OF  MAGNETISM  73 

Bunsen  flame,   and  again  test  it  by  means   of  the   compass. 
Record  the  effect. 

(b)  Heat  again  to  redness,  and  then  transfer  it  quickly  to  a 
position  between    the   poles    of   a  horseshoe    magnet.    Let  it 
remain  there  until  cool  and  test  again  with  the  compass. 

(c)  Explain  both  of  the  effects  on  the  assumption  that  mag- 
netization consists  in  a  particular  arrangement  of  the  molecular 
magnets.     (Remember  that  the  molecules  of  the  needle  are  set 
into  violent  agitation  when  the  needle  is  heated  to  redness.) 

V.  Making  a  magnet  by  induction,  (a)  Hold  a  short  piece  of 
unmagnetized  knitting  needle  or  a  small  steel  nail  between  the 
poles  of  a  horseshoe  magnet  and  tap  it  vigorously  with  some 
heavy  object  without  allowing  it  to  touch  the  magnet.  Remove 
it  and  test  its  poles  with  the'  compass  needle. 

(b)  Turn  it  end  for  end,  replace  it  between  the  poles  of  the 
horseshoe  magnet,  and  tap  again.    Record  the  change  which  you 
observe  in  its  poles. 

(c)  Remove  the  steel  rod  from  a  tripod  or  take  one  of  the 
small  steel  rods  used  for  bending  in  Experiment  12.    Hold  it 
nearly  vertical  in  a  north-and-south  plane,  the  upper  end  being 
tilted  20°  or  30°  toward  the  south.    Strike  the  upper  end  three 
or  four  sharp  blows  with  a  hammer  and  then  test  the  two  ends 
of  the  rod  for  magnetism.    Note  which  end  is  an  N  pole. 

(d)  Repeat  with  the  ends  of  the  rod  reversed.    Which  end  is 
now  an  jVpole?    Explain  on  the  assumption  that  the  molecules 
are  permanent  magnets  and  that  magnetization  consists  in  an 
alignment  of  these  molecules. 

From  all  of  the  above  experiments,  what  picture  do  you  make 
to  yourself  regarding  the  operations  which  go  on  within  a  bar 
of  iron  when  it  is  magnetized?  Draw  a  diagram  to  represent 
the  probable  arrangement  of  the  molecular  magnets  in  a  mag- 
netized bar,  and  another  to  represent  some  possible  arrangement 
in  an  unmagnetized  bar. 


74  LABORATORY  PHYSICS 

EXPERIMENT   27 
STATIC   ELECTRICAL   EFFECTS 

To  make  an  electroscope  bend  a  piece  of  No.  18  copper  wire 
into  the  form  shown  in  Fig.  39,  thrust  it  through  a  rubber 
stopper,1  hang  a  piece  of  aluminum  foil  about 
2  in.  long  over  .the  horizontal  part  of  the  wire, 
and  insert  in  a  glass  flask  as  shown.2 

I.  Conductors  and  nonconductors,  (a)  Attach 
one  of  the  steel  balls  of  Experiment  3  to  a  silk 
thread  by  means  of  sealing  wax,  or  simply  stick 
I  ~  a  penny  to  the  end  of  a  glass  rod  with  the  aid 
of  sealing  wax.  Such  an  arrangement  is  called  a 
proof  plane.  Charge  this  proof  plane  by  letting  it  rub  along  a 
stick  of  sealing  wax  which  has  been  electrified  by  being  rubbed 
with  flannel;  then  touch  it  to  the  wire  of  the  electroscope. 
What  does  the  instant  divergence  of  the  leaves  show  regarding 
the  ease  with  which  a  charge  of  electricity  passes  through  this 
metal  wire  ?  What  does  the  fact  that  the  leaves  stand  apart 
show  regarding  the  nature  of  the  force  which  the  two  parts 
of  the  same  charge  going  to  the  two  leaves  exert  upon  each 
other? 

(b)  Touch  the  wire  of  the  electroscope  for  an  instant  with  a 
piece  of  sealing  wax  which  has  not  been  electrified.  Touch  it 
with  a  wooden  ruler.  Touch  it  with  your  finger.  Which  of 
the  three  conducts  off  the  charge  most  readily  ? 

1  If  the  rubber  stopper  has  not  a  hole  through  it  already,  you  can  easily  make 
one  with  a  hot  knitting  needle.    If  it  already  has  a  hole  which  is  too  large,  cover 
the  wire  with  sulphur  or  sealing  wax.    This  will  not  only  make  it  fit,  but  it  will 
also  improve  the  insulation. 

2  An  electroscope  so  made  will  hold  its  charge  for  hours,  even  in  summer. 
To  cut  the  foil  blow  it  out  flat  on  a  sheet  of  paper,  lay  another  sheet  on  top 
of  it,  leaving  one  edge  uncovered,  and  then  cut  off  a  strip  with  a  sharp  knife  or 
razor.    A  saw  stroke  will  work  best. 


STATIC;  ELECTRICAL  EFFECTS  75 

(c)  Charge  the  proof  plane  or  steel  ball,  again  touch  it  with 
the  finger,  and  then  try  to  charge  the  electroscope  with  it. 
Explain  why  the  rubbed  sealing  wax  holds  its  charge  when  it 
is  held  in  the  hand,  while  the  proof  plane  or  steel  ball  loses  its 
charge  as  soon  as  it  is  touched  with  the  finger. 

II.  Positive  and  negative  electricity,  (a)  Charge  the  electro- 
scope as  above,  then  bring  the  charged  sealing  wax  toward  it. 
Record  the  effect  produced  on  the  divergence  of  the  leaves. 
Explain  this  effect  in  view  of  the  fact  that  the  charge  on  the 
wire  of  the  electroscope  is  a  part  of  the  charge  which  was 
originally  on  the  sealing  wax  (see  I  (a)). 

(b)  Rub  a  glass  rod  with  silk,  then  bring  it  slowly  toward  the 
charged  electroscope.    Record  the  first  effect  observed.    (If  you 
bring  the  rod  too  close,  the  effect  will  be  reversed.)    In  order  to 
account  for  this  effect,  what  sort  of  a  force  must  we  now  assume 
the  charge  on  the  glass  rod  to  exert  upon  the  charge  on  the 
electroscope  ? 

A  charge  of  electricity  which  acts  as  does  the  charge  on  a 
glass  rod  which  has  been  rubbed  with  silk  is  arbitrarily  called 
a  positive  (+)  charge.  A  charge  which  acts  like  the  charge  on 
the  sealing  wax  when  it  has  been  rubbed  with  flannel  is  called 
a  negative  (-— )  charge. 

(c)  Discharge  the  electroscope,  then  charge  it  with  the  aid  of 
the  proof  plane  and  glass  rod,  precisely  as  you  first  charged  it 
with  the  aid  of  the  proof  plane  and  sealing  wax.    Note  and 
record  the  behavior  of  the  leaves  when  you  now  bring,  first 
the  glass  rod,  and  then  the  charged  sealing  wax  toward  the 
electroscope..  In  view  of  all  these  observations,  state  how,  in 
general,  like  and  unlike   charges   of  electricity   act  upon  one 
another. 

(d)  Charge  the  electroscope  either  positively  or  negatively ; 
then  rub  a  piece  of  paper  on  the  coat  sleeve  and  determine  by 
bringing  the  paper  near  the  electroscope  whether  it  has  received 


76  LABORATORY  PHYSIOS 

a  +  or  a  —  charge.  Flick  your  handkerchief  across  the  sus- 
pended steel  ball  and  see  whether  it  has  received  a  +  or  a  — 
charge. 

III.  To  charge  two  bodies  simultaneously  by  induction.  Hold 
two  suspended  steel  balls  in  contact.    Bring  a  piece  of  electri- 
fied sealing  wax  to  within  an  inch  of  the  balls,  holding  it  in  the 
line  joining  their  centers.    While  it  is  in  this  position  separate 
the  two  balls,  then  bring  each  over  a  negatively  charged  electro- 
scope.   Has  the  ball  which  was  nearest  the  sealing  wax  received 
a  +  or  a  —  charge  ?    Record  the  sign  of  the  charge  on  the  other 
ball.    If  an  uncharged  body  contains  equal   amounts  of  both 
positive  and  negative  electricity  which,  under  ordinary  circum- 
stances,   are    so    uniformly   distributed    that   they    completely 
neutralize  each  other,  and  if  one  or  both  of  these  electricities 
is  free  to  move  through  the  body  under  the  influence  of  an 
outside  charge,  can  you  account  for  the  effects  which  you  have 
observed  ? 

IV.  To   charge  the   electroscope   by   induction.    Bring    the 
charged  sealing  wax  near  enough  to  the  electroscope  to  produce 
a  large  divergence.    Remove  the  sealing  wax.    Why,  on  the 
above  assumptions,  do  the  leaves  again  collapse  ?   Again  produce 
the  divergence,  but  now  touch  the  finger  to  the  electroscope 
before  removing  the  wax.    Why  do  the  leaves  collapse?    Re- 
move the  finger,  then  remove  the  wax.    Why  do  the  leaves  now 
diverge?    With  the  charged  sealing  wax  find  whether  in  charg- 
ing an  electroscope  by  induction  as  above  the  charge  imparted 
to  the  electroscope  is  like  or  unlike  that  of  the  charging  body. 
Repeat  with  the  glass  rod,  and  state  a  general  rule  for  the  sign 
of  the  charge  of  an  electroscope  which  has  been  charged  by  in- 
duction.   State  the  rule  for  charging  by  conduction  (see  I). 

V.  To  show  that  a  charge  is  on  the  surface  of  a  conductor 
only.  Place  the  inner  vessel  of  the  calorimeter  of  Experiment  18 
on  two  sticks  of  sealing  wax  which  rest  upon  the  table,  then 


STATIC  ELECTRICAL  EFFECTS  77 

charge  this  vessel  by  rubbing  over  it  a  charged  rod  of  any  kind. 
Bring  one  of  the  suspended  steel  balls  into  contact  with  the  out- 
side of  the  metal  vessel,  then  cause  the  ball  to  approach  the 
electroscope.  Has  the  ball  received  a  charge  ?  Discharge  the 
ball  with  the  finger,  then  lower  it  carefully  into  the  metal 
vessel  till  it  rests  on  the  bottom.  Remove  it  and  see  whether  it 
is  now  charged.  Record  your  conclusion.  Why  was  it  neces- 
sary to  place  the  metal  vessel  on  the  sticks  of  sealing  wax  ? 

VI.  To  prove  that  +  and  —  electricities  appear  in  equal 
amount,  (a)  Charge  a  steel  ball  negatively  and  bring  it  care- 
fully inside  of  vessel  A  (Fig.  40),  which  is  connected  by  a  wire 
to  the  electroscope.  The 
divergence  of  the  leaves 
will  measure  the  charge 
induced  on  the  outside  of 
A.  Touch  the  ball  to  the 
inner  wall  of  the  vessel. 

/         -ZJU-        \ 

The  divergence   of  the    t- ' 

leaves  is  now  a  measure 

of  the  charge  which  was  originally  on  the  ball,  for  by  V  this 
charge  has  all  passed  to  the  outside.  Did  the  divergence  change 
at  all  when  the  ball  touched  the  wall?  What  conclusion  do 
you  draw  regarding  the  minus  charge  on  the  ball  and  the  minus 
charge  induced  by  it  on  the  outside  of  the  vessel  ? 

(b)  Recharge  the  ball  and  again  hold  it  inside  of  A,  without 
touching  the  wall,  and  note  the  divergence  of  the  leaves.  Touch 
the  outside  of  A  with  the  finger.  Remove  the  finger,  then 
remove  the  ball,  but  do  not  discharge  it.  Is  the  deflection  the 
same  as  before?  Test  the  sign  of  the  charge  on  the  leaves. 
Reinsert  the  ball  and  touch  it  to  the  vessel.  Does  the  electro-' 
scope  show  any  charge?  What  conclusion,  then,  do  you  draw 
regarding  the  —  charge  on  the  ball  and  the  +  charge  which  was 
induced  on  the  inside  of  A  ? 


78  LABORATORY  PHYSICS 

VII.  The  principle  of  the  condenser,  (a)  By  means  of  a  wire 
connect  the  electroscope  with  a  vertical  metal  sheet  A  (Fig.  41), 
about  4  in.  square,  which  is  nailed  to  a  piece  of  wood  as  shown. 
Support  this  on  two  pieces  of  sealing  wax.  Charge  plate  A  by 
giving  it  a  single  stroke  with  a  small  piece  of  electrified  sealing 
wax.  If  the  electroscope  shows  any  leak,  rub  the  sealing-wax 
supports  on  a  cloth  until  they  are  warm.  Now  move  a  second 
plate  B,  which  you  keep  in  contact  with  your  hand,  up  to  within 
about  1  mm.  or  2  mm.  of  A.  What  effect  do  you  find  that  this 
/-^  has  on  the  potential  of  A  ? 

V— — /    x.  (Consider  potential  to  be 

/— 1-\          x^  A  B  measured  by  the  diver- 

gence of  the  leaves  of  the 
electroscope.) 

(b)  Electrify  the  sealing 
wax  again,  as  nearly  as  pos- 
sible in  the  way  you  did  at 

first,  and  give  A  another  stroke.  Repeat  until  the  original  diver- 
gence is  reestablished.  From  the  number  of  these  strokes  estimate 
roughly  how  many  times  the  electrical  capacity  of  A  has  been 
increased  by  the  presence  of  J5,  i.e.  how  many  times  the  original 
amount  of  electricity  is  now  required  to  bring  it  to  the  same 
potential  which  it  had  at  first.  In  view  of  the  fact  that  the 
—  charge  on  A  repelled  negative  electricity  to  the  earth  through 
your  finger,  and  thus  induced  a  +  charge  on  B,  can  you  see  why, 
when  B  is  near  by,  it  takes  a  larger  charge  on  A  to  produce  a 
given  divergence  than  when  B  is  remote  ? 

(c)  Slip  a  5  in.  x  5  in.  glass  plate  between  A  and  B  and  watch 
the  electroscope.  Does  this  increase  or  decrease  the  potential 
of  A?  Hence  does  it  increase  or  decrease  the  capacity  of  the 
condenser  ? 

Push  the  plates  together  until  each  is  in  contact  with  the 
glass  plate.  Remove  the  glass  without  changing  the  distance 


THE  VOLTAIC  CELL  79 

between  the  plates,  and  charge  A  to  a  given  divergence.  Insert 
the  glass  and  find  how  many  more  approximately  equal  charges 
may  now  be  put  on  A  before  bringing  the  leaves  to  about  the 
same  divergence.  The  ratio  of  the  charge  on  A  when  the  glass 
was  in  to  the  charge  when  the  glass  was  out  is  called  the  specific 
inductive  capacity  of  glass. 


EXPERIMENT  28 
THE  VOLTAIC   CELL 

I.  Action  of  dilute  sulphuric  acid  on  copper  and  zinc  strips. 
(a)  Open  circuit.    Fill  a  tumbler  two  thirds  full  of  water  and 
add  about  one  sixtieth  as  much  sulphuric  acid.    Introduce  a 
strip  of  zinc  about  a  centimeter  wide  into  the  acid,  and  observe 
and  record  what  effect,  if  any,  is  produced  by  the  acid.     (The 
bubbles  are  hydrogen.) 

Repeat  the  experiment  with  a  similar  strip  of  copper. 

Next  place  both  the  zinc  and  copper  in  the  acid  at  the  same 
time,  but  take  care  that  they  do  not  touch  each  other  at  any 
point.  Observe  and  record  the  action  at  each  plate. 

(b)  Closed  circuit.  Press  the  tops  of  the  strips  firmly  together 
and  notice  what  change,  if  any,  takes  place  at  the  surface  of 
each  metal.  Record  results. 

II.  Effect  of  amalgamation.    Dip  the  zinc  plate  into  a  dish 
containing  a  little  mercury  and  rub  the  mercury  over  the  wet 
portion  of  the  zinc  until  it  is  covered  with  a  smooth,  even  coat 
of  mercury.     Dip  the  amalgamated  zinc  into  the  sulphuric-acid 
solution  again,  and  repeat  the  observations  of  I,  recording  what 
differences,  if  any,  are  observed  in  the  action. 

III.  Effects  observable  about  the  wire  connecting  the  strips. 
(a)  For  convenience  in  handling,  place  strips  of  copper  and 
of  amalgamated  zinc  in  clamps  such  as  those  shown  in  Fig.  42, 


80 


LABORATORY  PHYSICS 


and  connect  these  clamps  by  means  of,  say,  No.  24  copper  wire 
to  the  binding  posts  of  the  25-turn  coil  of  No.  22  wire  on  the 
galvanoscope,  after  placing  the  latter  with  the  plane  of  its  coils 
north  and  south.  Dip  the  metals  in  the  acid  and  observe  the 
effect  on  the  needle. 

(b)  Disconnect  the  wires  from  the  galvanoscope  and  touch 
them  to  the  tongue.    What  evidence   do  you  obtain  of  some 


action  going  on  when  the  plates  are  in  the   acid,  but  which 
disappears  as  soon  as  they  are  lifted  from  it? 

IV.  Polarization.  Take  a  fresh  and  dry  copper  plate,  or 
else  dry  the  old  one  by  heating  it  in  a  Bunsen  flame  until  it  is 
much  too  hot  to  hold,  and  then  letting  it  cool.  Insert  the  zinc 
and  copper  in  the  clamps  and  connect  as  before  to  the  25-turn 
coil  of  the  galvanoscope,  but  this  time  insert  into  the  circuit 
about  a  meter  of  No.  36  German  silver  wire.1  (No.  30  will  do, 
but  No.  36  is  better.)  Turn  the  compass  until  the  needle  points 
to  0° ;  then  immerse  the  plates  in  the  acid,  and  as  soon  as  the 
needle  stops  swinging  violently  read  the  deflection.  (If  this 
deflection  is  more  than  40°  or  50°,  slide  the  compass  along  in  the 

1  For  the  sake  of  avoiding  loose  German  silver  wire,  it  is  best  to  insert  the 
meter  of  No.  36  wire  between  the  binding  posts  ac  of  Fig.  52,  and  then  to  con- 
nect the  zinc  plate  of  the  cell  to  a,  the  copper  plate  to  one  terminal  of  the  gal- 
vanoscope, and  the  other  terminal  of  the  galvanoscope  to  c. 


THE  VOLTAIC  CELL  81 

frame  away  from  the  25-turn  coil,  until  the  deflection  is  reduced 
to  50°  or  less.)  Watch  the  needle  for  a  minute  and  record  what 
you  observe.  In  II  you  found  that  if  the  zinc  is  well  amalga- 
mated, hydrogen  appears  only  at  the  copper  plate.  Short-circuit 
the  cell  for  half  a  minute  by  holding  a  short  strip  of  copper  in 
contact  with  both  the  copper  and  the  zinc  plates.  This  simply 
enables  the  hydrogen  to  be  generated  in  greater  abundance.  It 
brings  the  deflection  nearly  to  o  because  most  of  the  current 
now  goes  through  the  copper  strip.  Remove  the  copper  strip. 
Does  the  deflection  return  quite  to  its  old  value  ?  From  these 
experiments,  what  effect  do  you  conclude  that  the  accumula- 
tion of  hydrogen  upon  the  copper  plate  has  upon  the  strength 
of  the  current  which  the  cell  can  furnish  ?  This  is  technically 
called  the  polarization  of  the  cell,  and  a  cell  in  which  this  effect 
occurs  is  called  a  polarizing  cell. 

V.  A  nonpolarizing  cell.  Replace  the  simple  cell  by  a  Daniell 
cell,  or  construct  what  is  essentially  a  Daniell  cell  as  follows. 
First  dry  the  copper  plate  in  the  Bunsen  flame,  then  replace 
it  in  its  clamp.  Fill  the  tumbler  half  full  of  a  saturated  solu- 
tion of  copper  sulphate,  and  pour  zinc  sulphate  into  a  small  porous 
cup,  which  is  then  to  be  placed  inside  the  tumbler.  Now  immerse 
the  plates  in  the  liquids,  the  zinc  going  into  the  zinc  sulphate 
in  the  porous  cup  and  the  copper  into  the  copper  sulphate.  (The 
porous  cup  is  simply  to  keep  the  two  liquids  separated.  The 
electric  current  can  pass  through  it  with  ease.)  Watch  the  needle 
and  record  its  behavior.  Short-circuit  the  cell  and  see  if  there- 
after the  deflection  returns  to  its  old  value.  Is,  then,  a  Daniell 
cell  a  polarizing  or  a  nonpolarizing  cell  ?  Does  the  fact  that  the 
element  which  is  deposited  on  the  copper  plate  when  it  is  im- 
mersed in  copper  sulphate  is  copper  itself  suggest  to  you  any 
reason  why  in  this  case  the  current  is  not  changed,  as  was  found 
to  be  the  case  when  the  deposit  was  hydrogen  ?  In  which  case  is 
the  character  of  the  surface  of  the  plate  changed  by  the  deposit  ? 


82  LABORATORY  PHYSICS 

VI.  A  polarizing  commercial  cell.  Replace  the  Daniell  by  a 
Leclanche  cell,  if  one  is  available  (a  dry  cell  will  answer  nearly 
as  well).  This  consists  of  a  zinc  rod  in  sal  ammoniac  and  a 
carbon  plate  inside  a  porous  cup  which  is  full  of  manganese 
dioxide.  See  first  whether  the  current  which  this  cell  sends 
through  the  three  feet  of  No.  36  German  silver  wire  weakens 
at  all  in  two  minutes.  (If  the  deflection  is  more  than  45°, 
push  the  compass  farther  away  or  change  to  the  one-turn  coil.) 
Then  short-circuit  the  cell  for  half  a  minute  and  see  if  there- 
after the  deflection  returns  to  the  old  value.  Is,  then,  this  cell 
polarizing  or  nonpolarizing?  Watch  the  needle  for  a  minute 
after  the  cell  has  been  short-circuited.  Does  the  current  gradu- 
ally recover  part  of  its  former  strength?  Break  the  circuit 
entirely  and  let  the  cell  stand  for  a  few  minutes;  then  read 
the  deflection. 

Try  the  same  experiment  with  a  simple  cell.  Record  the 
difference  in  the  behavior  of  the  two  cells.  This  difference  is 
due  to  the  fact  that  in  the  simple  cell  there  is  nothing  to  remove 
the  film  of  hydrogen  from  the  surface  of  the  plate  upon  which  it 
is  deposited.  In  the  Leclanche  cell,  on  the  other  hand,  the  man- 
ganese dioxide  slowly  unites  with  and  therefore  removes  the 
hydrogen  from  the  carbon  plate.  This  is  indeed  the  object  of 
its  use.  A  Leclanche  cell  is,  then,  one  which  recovers  on  open 
circuit. 


EXPERIMENT   29 
MAGNETIC  EFFECT  OF  A  CURRENT 

I.  The  right-hand  rule,  or  Ampere's  rule.  Since  a  wire 
through  which  a  current  is  flowing  has  just  been  found  to 
deflect  a  magnetic  needle  held  near  it,  the  wire  must  be  sur- 
rounded by  magnetic  lines  of  force.  The  direction  in  which  the 


MAGNETIC  EFFECT  OF  A  CUBEENT 


83 


FIG.  43 


N  pole  of  the  magnetic  needle  tends  to  move  gives,  by  definition, 
the  direction  of  these  magnetic  lines. 

The  direction  in  which  the  positive  electricity  flows  through 
the  circuit  of  a  zinc-copper  cell  is  from  zinc  to  copper  inside  the 
liquid  and  from  copper  to  zinc  in 
the  connecting  wire,  i.e.  it  flows  in 
the  direction  in  which  the  hydro- 
gen was  found  to  move  in  the  last 
experiment.  We  know  this  be- 
cause a  very  delicate  electroscope  will  show  that  on  open  cir- 
cuit the  copper  plate  acquires  a  small  +  charge  of  static  elec- 
tricity and  the  zinc  a  small  —  charge.  For  this  reason  the  copper 
or  carbon  plate  of  a  voltaic  cell  is  always  called  the  plus  (+) 
plate  and  the  zinc  the  minus  (— )  plate.  The  direction  of  an 
electric  current  is  defined  as  the  direction  in  which  the  positive 
electricity  moves. 

By  the  series  of  experiments  given  below,  test  the  following 
rule.  If  the  conductor  is  grasped  by  the  right  hand  so  that  the 
thumb  points  in  the  direction  in  which  the  current  flows,  then  the 
magnetic  lines  of  force  pass  in  con- 
centric circles  around  the  wire  in 
the  direction  in  which  the  fin- 
gers of  the  hand  encircle 
it  (Fig.  43). 


(a)  Connect  either  a  simple  cell  or  a  dry  cell  in  the  manner 
shown  in  Fig.  44,  so  that  the  current  will  flow  from  the  copper 


84  LABORATORY  PHYSICS 

(or  carbon)  through  the  commutator  C,  then  over  the  needle 
from  south  to  north,  and  back  through  the  commutator  to  the 
zinc.  All  of  the  connecting  wires  should  be  copper,  for  exam- 
ple No.  24,  and  that  to  the  right  of  the  commutator  should  be 
10  ft.  or  12  ft.  long.  Insert  the  top  of  the  commutator  and 
record  the  direction  in  which  the  north  pole  of  the  needle 
turns. 

(b)  Turn  the  top  of  the  commutator  through  90°,  so  that  the 
mercury  cup  a  is  connected  to  e  and  b  to  c?,  instead  of  a  to  b 
and  e  to  d.    This  reverses  the  current  in  the  wire  so  that  it 
goes  over  the  needle  from  north   to  south.    Record  the  effect 
on  the  needle  and  compare  with  Ampere's  rule. 

(c)  Place  the  compass  above  the  wire  without  changing  the 
direction  of  the  current,  and  compare  with  the  rule  the  effect 
produced  on  the  needle.    Reverse  the  direction  of  the  current 
by  means  of  the  commutator  and  again  compare. 

(d)  Hold  the  wire  so  that  the  current  flows  vertically  down- 
ward just  in  front  of  the  N  pole  of  the  compass ;  then  cause 
the  current  to  flow  upward  past  the  same  pole,  and  test  the 
rule  in  each  case. 

(e)  Hold  the  wire  so  that  the  current  flows  from  west  to  east 
over  the  middle  of  the  needle. 

Does  the  experiment  show  that  the  lines  of  magnetic  force 
lie  in  planes  at  right  angles  to  the  direction  of  the  wire  ?    How  ? 

II.  To  find  the  direction  of  an  unknown  current.    Let  the 
instructor  bring  a  current  the  direction  of  which  is  unknown 
into  the  laboratory  by  a  wire  connected  with  a  cell  in  a  closet 
or  in  an  adjoining  room.    Hold  a  compass  needle  near  the  wire 
and  determine  the  direction  in  which  the  current  is  flowing  in 
the  wire.    Record  your  result  and  then  test  the  correctness  of 
it  by  following  the  wire  to  the  cell. 

III.  The  effect  of  loops,    (a)   As  in  I,  pass  a  current  from 
a  cell  over  the  compass  from  south  to  north,  keeping  the  wire 


MAGNETIC  PROPERTIES  OF  COILS  85 

as  close  to  the  face  of  the  compass  as  possible.    Note  the  amount 

of  deflection.    Then  cause  the  wire  to  return  beneath  the  needle, 

so   that    a   loop  is 

formed,  in  the  upper 

part  of  which  the 

current  flows   past 

the  needle  from  south  to  north  and  in  the  lower  part  from 

north  to  south.    Is  the  deflection  greater  or  less  than  at  first? 

Why? 

(b)  Try  the  effect  of  placing  both  sides  of  the  loop  above  the 
needle,  as  in  Fig.  45.    Explain  the  observed  effect. 

(c)  Loop  the  wire  several  times  around  the  compass  in  such 
a  way  that  the  plane  of  the  coil  is  north  and  south.    What 
change   is    produced    in    the    deflection    by    each    new    turn? 
Explain. 

EXPERIMENT  30 
MAGNETIC  PROPERTIES  OF  COILS  CARRYING  CURRENTS 

I.  Magnetic  effect  of  a  helix,  (a)  Having  the  circuit  arranged 
as  in  Fig.  44,  the  current  being  furnished  either  by  a  simple 
cell  or  by  a  dry  cell,  form  a  close  helix  (see  Fig.  46)  by  wrap- 
ping the  conducting  wire  forty  or  fifty  times  around  a  lead 
pencil.  Then  with  the  aid  of  the  compass 
see  whether  or  not  the  helix  is  a  magnet, 
i.e.  whether  one  end  of  it  attracts  the  north 
pole  while  the  other  repels  it. 

(b)  By  means  of  the  commutator  reverse 
FlG-  46  the   direction  of  the    current  through  the 

helix  and  record  what  effect  is  thus  produced  upon  the  poles. 
(c}  Test  the  following  rule  for  determining  the  poles  of  a 
helix.    If  the  helix  is  grasped  in  the  right  hand  so  that  the  fingers 
are  pointing  in  the  direction  in  which  the  current  is  flowing  in  the 


86 


LABORATOKY  PHYSICS 


V      \      'vOOnOCYXYl 


coils  (see  Fig.  47),  the  thumb  will  point  in  the  direction  of  the 
magnetic  lines  of  force,  i.e.  the  thumb 
will  point  towards  the  north  pole  of 
the  helix.  Show  how  this  rule  fol- 
lows from  Ampere's  rule. 

II.  The  principle  of  the  electro- 
magnet, (a)  Thrust  an  unmagnet- 
ized  soft  iron  rod,  e.g.  a  wire  nail, 
into  the  helix  and  then  test  the  nail 
and  helix  together  in  the  same  way 
in  which  the  helix  alone  was  tested 

in  the  preceding  experiment.    Are  the  poles  stronger  or  weaker 

than  before? 

(b)  Reverse  the  current  by  means  of  the  commutator  and  test 
and  record  the  effect  on  the  poles. 

(c)  Bend  a  piece  of  large  iron  wire  into  the  shape  of  a  letter 
U  and  mark  one  end  with  chalk.    About  the  ends  of  both  arms 


FIG.  47 


FIG.  48 


of  the  U  wind  a  wire  carrying  a  current,  in  such  a  way  that 
the  "marked  end  of  the  U  shall  be  an  N  magnetic  pole  and  the 
other  an  S  pole.  Test  by  means  of  a  compass. 


ELECTBOMOTIVE  FORCES  87 

III.  Principle  of  the  D'Arsonval  galvanometer,  (a)  Hang  a  coil 
of  about  one  hundred  and  seventy-five  turns  of  No.  32  copper 
wire  between  the  poles  of  a  horseshoe  magnet  in  the  manner 
shown  in  Fig.  48,  so  that  the  plane  of  the  coil  is  parallel  to 
the  line  joining  the  poles.  The  two  wires  which  run  from  the 
coil  up  to  the  cork  support  should  be  of  No.  40  insulated  copper, 
and  one  of  them  should  be  twisted  about  the  other  loosely,  as 
in  the  figure.  Pass  a  current  from  a  cell  first  through  a  commu- 
tator and  then  through  the  coil.  Record  the  effect  observed  in 
the  coil. 

(b)  Reverse  the  direction  of  the  current  and  observe  the  effect 
produced.    Explain  why  the  coil  turns  as  it  does,  remembering 
that  it  is  nothing  but  a  flat  helix. 

(c)  By  rotating  the  cork  at  the  top,  set  the  coil  between  the 
poles  of  the  magnet  in  such  a  way  that  its  plane  is  perpen- 
dicular to  the  line  joining  these  poles.    Turn  on  the  current 
and  note  the  effect. 

(d)  Reverse  the  current  and  note  again  the  effect.    Explain 
in  each  case  the  effect  observed. 


EXPERIMENT    31 
ELECTROMOTIVE   FORCES 

In  the  present  experiment  we  shall  compare  the  electromotive 
forces,  or  the  electric  pressures,  which  cells  of  different  form  are 
able  to  maintain,  by  comparing  the  currents  which  they  can 
force  through  a  long  piece  of  fine  wire  (a  large  resistance). 

I.  Effect  of  size  of  plates  and  distance  between  them  on  the 
electromotive  force  of  a  cell.  To  one  of  the  terminals  of  the  100-. 
turn  coil  of  the  galvanoscope  connect  a  small  coil  R  (Fig.  49) 
of  German  silver  wire  the  resistance  of  which  is  about  1000 
ohms.  Then  complete  the  circuit  of  the  simple  cell  through  this 


88 


LABORATORY  PHYSICS 


high-resistance  galvanometer  in  the  manner  shown,  and  read  the 
deflection  of  the  needle.  If  it  is  more  than  20°,  push  the  com- 
pass farther  away  from  the  coil.  Lift  the  plates  almost  out 
of  the  liquid,  and  read  again.  Disconnect  the  wires  from  the 
binding  posts  of  the  cell,  remove  the  frame  and  plates  from 
the  tumbler,  press  the  wires  very  firmly  against  much  narrower 
zinc  and  copper  strips  than  those  used  before,  immerse  these 
in  the  liquid,  and  read  again.  Place  these  strips  as  far  apart  in 
the  tumbler  as  you  can,  and  see  if  the  deflection  changes  as  you 
move  them  together.  (In  all  cases  in  which  accurate  readings 
of  deflections  are  to  be  taken  it  is  desirable  to  tap  the  frame  of 


the  galvanometer  lightly  with  a  pencil  so  as  to  overcome  any 
tendency  which  the  needle  may  have  to  stick.) 

What  conclusions  do  you  draw  in  regard  to  the  effect  of  the 
distance  between  the  plates  and  the  area  of  immersion  of  the 
plates  on  the  electromotive  force  of  a  cell? 

II.  Effect  of  different  metal  plates  on  the  electromotive  force 
of  a  cell,  (a)  Without  changing  anything  else  in  the  circuit, 
insert  in  the  clamp  of  the  simple  cell  a  lead  plate  in  place  of 
the  copper  plate  of  the  above  experiment.  If  the  needle  is 
deflected  in  the  same  direction  as  before,  we  may  know  that  in 
the  external  circuit  the  current  flows  from  the  lead  to  the  zinc, 
i.e.  that  lead  in  sulphuric  acid  is  +  with  respect  to  zinc  r  but 


ELECTROMOTIVE    FORCES  89 

if  the  needle  turns  in  the  opposite  direction,  then  the  zinc  is  -f 
with  respect  to  the  lead.  Record  tests  with  zinc-lead,  zinc-car- 
bon, and  zinc-aluminum  electrodes  in  the  following  form : 

Zinc  -     Copper  +      Deflection  12°     Zinc  ?       Lead  ?       Deflection  ? 

Zinc  ?       Carbon  ?       Deflection    ?        Zinc  ?       Aluminum  ?       Deflection  ? 

(b)  Replace  the  zinc  by  a  lead  plate,  and  record  tests  on  lead- 
copper,  lead-aluminum,  and  lead-carbon  thus  : 

Lead  ?  Copper        ?  Deflection  ? 

Lead  ?  Aluminum  ?  Deflection  ? 

Lead  ?  Carbon        ?  Deflection  ? 

Do  you  see  any  connection  between  the  results  in  (a)  and  (b) 
which  enables  you  to  predict  all  the  results  in  (b)  from  those 
in  (a)? 

If  so,  arrange  these  five  substances  in  a  list  such  that  each 
substance  will  be  positive  with  respect  to  any  substance  below 
it  in  the  list,  but  negative  with  respect  to  any  substance  above 
it.  Which  pair  give  the  highest  E.M.F.  ?  What  conclusion  do 
you  draw  in  regard  to  the  effect  on  the  E.M.F.  of  the  kind  of 
plates  used  ? 

III.  Effect  of  different  liquids  (electrolytes)  on  the  E.M.F. 
Measure  the  deflection  again,  using  the  same  galvanoscope, 
when  zinc  and  copper  are  immersed  (a)  in  dilute  sulphuric  acid 
(H2SO4) ;  (b)  in  a  solution  of  common  salt  (NaCl,  i.e.  sodium 
chloride) ;  (<?)  in  a  solution  of  sodium  carbonate  (Na2CO3) ; 
(d)  in  common  water  (H2O). 

Rinse  the  plates  thoroughly  before  placing  them  in  a  new 
liquid. 

Now  place  copper  and  iron  strips  in  the  clamps  of  the  cell, 
immerse  in  the  sulphuric-acid  solution,  and  read ;  then  immerse 
the  same  strips  in  a  weak  solution  of  ammonium  sulphide 
(NH4)2S.  What  effect  has  the  change  in  the  liquid  had  upon 
the  direction  of  the  current  ? 


90 


LABORATORY  PHYSICS 


What  conclusion  do  you  draw  in  regard  to  the  effect  of  the 
electrolyte  on  the  direction  and  magnitude  of  the  E.M.F.  of 
a  cell? 

IV.  Effect  of  series  and  parallel  connection  on  the  E.M.F.  of 
the  combination,  (a)  Connect  the  high-resistance  circuit  to 


Fio.  60 

the  terminals  of  a  single  cell  arid  read  the  deflection.  If  this 
is  more  that  8°  or  10°,  push  the  compass  away  from  the  coil 
until  it  is  reduced  to  about  this  value.  (The  object  of  making 
the  deflection  small  is  to  arrange  the  conditions  so  that  the 
E.M.F.  may  be  taken  as  proportional  to  the  deflections.) 

Join  two  similar  cells  in  series,  i.e.  the  zinc  of  one  to  the 
copper  of  the  other  (Fig.  50),  and  read  the  deflection  when 

connected  to  the 
same  circuit. 

(b)  Connect  the 
two  similar  cells 
in  parallel,  i.e. 
zinc  to  zinc  and 
copper  to  copper 


p,o.  5i 


fl 

read  the  deflec- 
tion, and  compare  with  that  produced  by  a  single  cell. 

What  conclusions  do  you  draw  in  regard  to  the  effects  of 
series  and  parallel  connections  on  E.M.F.? 


OHM'S  LAW  91 

V.  Electromotive  forces  of  various  commercial  cells.  Hav- 
ing the  galvanometer  circuit  arranged  as  in  Fig.  49,  reduce  the 
deflection  produced  by  a  Daniell  cell,  improvised  as  in  Experi- 
ment 28,  IV,  to  about  10°  by  moving  the  compass  away  from 
the  coil ;  then  find  the  deflections  produced  by  a  dry  cell,  a  Le- 
clanche  cell,  and  any  other  cells  which  you  may  have,  and  calcu- 
late the  E.M.F.  of  all  the  latter  cells  on  the  assumption  that 
the  E.M.F.  of  a  Daniell  cell  is  1.08  volts.  In  this  work,  how- 
ever, be  very  careful  not  to  change  the  galvanoscope  in  any 
way  during  any  of  the  operations. 


EXPERIMENT  32 
OHM'S  LAW 

I.  To  prove  that  if  the  current  remains  constant  in  a  circuit 
the  ratio  of  the  E.M.F.  to  the  resistance  must  remain  constant 
also.  (<t)  Let  the  Daniell  or  dry  cell  be  connected  to  the  ter- 
minals of  the  high-resistance  galvanoscope  coil,  through  the 
1000-ohm  German  silver  coil,  and  let  the  deflection  be  care- 
fully noted. 

(b)  Let  two  cells  be  connected  in  series  and  joined  to  the 
same  high-resistance  galvanoscope  circuit.    The  deflection  will, 
of  course,  be  found  to  be  much  increased.    Then  introduce  into 
the  circuit  a  second  precisely  similar  galvanoscope  coil  with  its 
German  silver  wire  in  series  with  the  one  already  there.    Is  the 
current  reduced  to  its  old  value  ? 

(c)  If  it  is  convenient,  introduce  three  cells  in  series  into  the 
circuit,  and  see  whether  the  introduction  of  a  third  galvano- 
scope coil  and  German  silver  wire  will  reduce  the  current  to  its 
old  value.    If  the  current  is  to  be  kept  constant,  how  do  these 
experiments  show  that  the  resistance  must  be  increased  as  the 
E.M.F.  is  increased? 


92  LABORATORY  PHYSICS 

II.  To  prove  that  if  the  E.M.F.  is  kept  constant  the  current 
will  be  inversely  proportional  to  the  resistance,  (a)  Pass  the 
current  from  a  Daniell  cell  through  the  commutator,  the  high- 
resistance  coil  of  the  galvanoscope,  and  the  1000-ohm  coil  of 
German  silver  wire,  all  arranged  in  series.  If  the  deflection 
of  the  compass  needle  is  more  than  12°  or  14°,  push  the  com- 
pass away  from  the  coil  until  its  deflection  is  reduced  to  this 
value.  Read  the  position  of  the  needle  carefully,  both  before 
and  after  reversing  the  direction  of  the  current  by  means  of 
the  commutator. 

(6)  Introduce  into  the  circuit  a  second  German  silver  coil  just 
like  the  first  and  a  second  galvanoscope  coil  similar  to  the  first, 

. ,£ 


FIG.  52 

all  being  joined  in  series.  The  resistance  of  these  two  sets  of 
coils  is  obviously  exactly  double  that  of  the  first  single  set. 
Read  the  deflections  of  the  needle  before  and  after  reversing 
the  direction  of  the  current.  How  has  the  current  been  changed 
by  doubling  the  resistance  ? 

III.  To  prove  that  when  a  constant  current  is  flowing  in  a 
circuit  the  potential  difference  between  any  two  points  in  the 
circuit  is  directly  proportional  to  the  resistance  between  these 
two  points.  (a)  Connect  a  Daniell  cell  B  (Fig.  52),  improvised  as 
in  Experiment  28,  IV,  to  the  ends  of  a  meter  of  No.  30  German 
silver  wire  mounted  above  a  meter  stick  ac.  Attach  one  end  of 
the  high-resistance  'coil  of  the  galvanoscope  G  to  the  binding 
post  a  and  press  the  other  end  firmly  down  upon  the  wire  at  a 


COMPARISON  OF  RESISTANCES  93 

point  just  10  cm.  from  a.  Read  carefully  and  record  the  deflec- 
tion. "(It  it  is  more  than  4°  or  5°,  reduce  it  to  this  amount  by 
pushing  away  the  compass.)  The  deflection  is  a  measure  of  the 
potential  difference,  i.e.  the  difference  in  electrical  pressure, 
between  the  ends  of  this  10-cm.  length  of  wire. 

(6)  Move  the  free  end  along  to  distances  of  20  cm.,  30  cm., 
and  40  cm.  from  a,  and  read  in  each  position.  The  resistance 
of  20  cm.  of  wire  is  obviously  twice  the  resistance  of  10  cm.,  etc. 
What  relation  do  you  find  to  exist  between  the  P.D.  and  the 
resistances  across  which  they  are  taken  ? 

The  above  experiment  proves  that  no  matter  in  what  ways 
the  resistance  R.  of  a  circuit,  the  current  C.  flowing  in  the  cir- 
cuit, or  the  P.D.  forcing  the  current  through  the  circuit,  are 
varied,  a  fixed  relation  always  exists  between  these  three  quan- 

P  D 

tities,  viz.  current  is  proportional  to  — '—-^  •    If  we  define  the  unit 

of  resistance  as  the  resistance  of  a  conductor  through  which 
one  ampere  of  current  flows  when  the  difference  in  electrical 
pressure  between  its  ends  is  one  volt,  then  we  may  write  the 
results  of  this  experiment  in  the  form 

P.D.       „  volts 

—  =  C.,    or     — =  amperes. 

R.  ohms 

This  is  Ohm's  law. 


EXPERIMENT  33 
COMPARISON  OF  RESISTANCES 

I.  To  find  the  relative  resistances  of  copper,  iron,  and  German 
silver  by  the  fall-of-potential  method,  (a)  Wind  up  into  a  coil 
C  (Fig.  53)  just  3  m.  of  No.  30  insulated  copper  wire.  Attach 
one  end  of  it  to  the  binding  post  E.  Between  the  binding  posts 
E  and  H  stretch  about  80  cm.  of  No.  30  iron  wire,  and  between 
H  and  F  stretch  about  20  cm.  of  No.  30  German  silver  wire. 


94  LABORATORY  PHYSICS 

Connect  the  terminals  of  the  dry  or  Daniell  cell  B  to  the  points 
a  and  F.  Then  join  the  terminals  of  the  high-resistance  coil  of 
the  galvanoscope  G  so  that  its  deflection  will  indicate  the  fall 
of  potential  through  the  copper  coil  C  (Fig.  53).  Read  the  deflec- 
tion of  the  galvanoscope  needle  very  carefully. 

(b)  Connect  to  E  the  end  of  the  galvanoscope  terminal  which 
was  before  at  a,  and  move  the  other  terminal  along  the  iron 
wire  toward  H  until  the  P.D.  between  E  and  the  point  touched 
is  the  same  as  that  between  a  and  E,  i.e.  until  the  galvanoscope 
deflection  is  the  same  as  at  flrst.  The  length  of  iron  wire 

^- -^ 


<*L_L1'.  1  '  '  '  '  1  •  '  '  '  I  '  •  '  '  I  '  • 

,  .  1  .  .  ,  ,  1  ,  ,  ,  ,  1  ,  ,  ,  ,]  ,  ,  ,  ,  1  ,  ,  .  ,  p 

23E3S     5    -     -      2    •        SS523] 

o  p 

FIG.  53 

between  the  galvanoscope  terminals  must  then,  by  Ohm's  law 

P  D          \ 

— — -=C. ),  have  exactly  the  same  resistance  as  the  3  m.  of 

copper  wire  in  the  coil  (7,  for,  since  the  P.D.  is  the  same  and  the 
current  is  the  same,  the  resistance  must  also  be  the  same.  Find, 
then,  by  computation  how  many  times  the  resistance  of  an  iron 
wire  exceeds  that  of  a  copper  wire  of  the  same  length  and 
diameter. 

(<?)  Attach  the  free  terminal  of  the  galvanoscope  at  F  and 
move  the  end  which  was  before  at  E  along  the  German  silver 
wire  until  the  deflection  is  the  same  as  before.  Compare  by 
computation  the  resistance  of  a  German  silver  wire  with  that 
of  a  copper  wire  of  the  same  length  and  diameter. 

II.  To  measure  an  unknown  resistance  by  means  of  Wheat- 
stone's  bridge.  If  a  current  is  made  to  divide,  as  at  a  (Fig.  54), 
so  that  part  of  it  flows  along  the  branch  abc  and  part  along  the 


COMPARISON  OF  RESISTANCES  95 

branch  adc,  then  there  will  be  a  continual  fall  in  potential  in 
going  from  a  to  c  over  each  branch.  Hence  for  any  point  b 
in  one  branch  there  must  be  a  corresponding  point  d  in  the 
other  branch  at  which  the  same  potential  exists.  If  these  two 
points  are  connected  through  a  galvanometer  G,  no  current  will 
flow  through  this  galvanometer,  since  the  same  electrical  pres- 
sure exists  at  b  as  at  d.  If  the  end  of  the  connecting  wire  is 
moved  a  little  to  the  right  of  d,  a  current  will  flow  in  one  direc- 
tion through  G :  while  if  it  is  moved  a  little  to  the  left,  a  current 
will  flow  through  G  in  the  opposite  direction.  Hence,  in  order 
to  find  experimentally  the  point 
d  which  has  the  same  potential 
as  the  point  6,  we  have  only 
to  move  the  end  of  the  galvan- 
ometer wire  along  the  branch 
adc  until  we  find  a  point  at  which 
the  galvanometer  shows  no  de- 
flection. When  this  point  has 
been  found  the  resistance  of 
the  four  branches  ad  (=  P)  dc,  FlG-  64 

(=  $),  ab  (=  R),  and  be  (=  X)  may  be  proved  to  be  related  in 
the  following  way : 

P/Q  =  R/X. 

To  prove  that  this  is  so,  we  have  only  to  apply  Ohm's  law. 
For  if  PDl  represents  the  potential  difference  between  a  and  c?, 
and  PZ>2  that  between  d  and  c,  then,  since  b  and  d  have  the 
same  potential,  PDl  will  also  represent  the  potential  difference 
between  a  and  d,  and  PZ>2  that  between  d  and  c.  Now,  by 
Ohm's  law,  since  the  same  current  Cl  is  flowing  through  ad 
and  dc,  we  have  C\  =  PDJP  =  PD^/Q,  or  PD^PD^  =  P/Q. 
Similarly,  on  the  lower  branch,  PDl/PD2  =  R/X.  Therefore, 
P/Q  =  R/X  and  X  =  P  x  R/Q. 


96  LABORATORY  PHYSICS 

(a)  Stretch  No.  30  German  silver  wire  between  a  and  c,  as  in 
Fig.  5(7,  place  a  meter  stick  beneath  it,  and  then  connect  a  simple 
or  a  dry  cell  B  to  the  terminals  a  and  c.  Between  the  binding 
posts  a  and  b  insert  some  known  resistance,  say  a  one-ohm 
coil.  Between  b'  and  c  insert  the  3-m.  coil  of  No.  30  copper 
wire  used  in  I.  The  brass  strap  between  b  and  b'  has  a  negli- 
gible resistance,  so  that  the  whole  of  it  may  be  considered  as 
the  point  b  of  Fig.  54.  Connect  to  the  binding  post  at  m  one 
terminal  of  a  D'Arsonval  galvanometer  G.  This  instrument 
is  precisely  that  shown  in  Fig.  48,  save  that  a  slender  pointer 
must  be  inserted  in  the  place  provided  for  it  (see  also  Fig.  57) 
for  the  sake  of  making  small  deflections  more  easily  observable. 


FIG.  65 


Touch  the  free  terminal  of  the  galvanometer  at  a  number 
of  points  along  the  wire  ac  until  you  find  that  point  at  which 
the  galvanometer  shows  no  deflection  on  making  contact.  Since 
the  wire  ac  is  uniform,  the  ratio  of  the  resistances  P  and  Q  is 
simply  the  ratio  of  the  lengths  ad  (=  IJ  and  dc  (=  /2).  Hence, 

X/R  =  lz/lv  or  X  =  R  x  yir 

(b)  In  the  same  way  measure  the  resistance  of  exactly  50  cm. 
of  No.  30  iron  wire,  and  calculate  from  the  result  the  resistance 
in  ohms  of  such  a  wire  3  m.  long.     By  what  does  the  value  thus 
found  for  the  relative  resistance  of  iron  and  copper  differ  from 
that  found  in  I  ? 

(c)  In  the  same  way  measure  the  resistance  of  exactly  25  cm. 
of  No.  30  German  silver  wire,  and  compute  from  the  result 


INTERNAL  RESISTANCE  OF  GALVANIC  CELLS      97 

the  resistance  of  such  a  wire  3  m.  long.    Record  the  per  cent  of 
difference  between  this  result  and  that  found  in  I. 

Tabulate  in  che  form  given  below  the  final  results  of  your 
measurements  upon  the  relative  resistances  of  the  three  metals, 
copper  being  taken  as  1. 


METAL 

FALL  OF  POTENTIAL 
METHOD 

BRIDGE  METHOD 

Copper 

1 

1 

Iron 

8.1 

7.9 

German  silver      .... 

17.8 

18.5 

EXPERIMENT  34 
INTERNAL  RESISTANCE  OF  GALVANIC  CELLS 

I.  Currents  furnished  by  galvanic  cells  when  the  external  re- 
sistance is  small.  In  the  experiment  on  E.M.F.  (Experiment  31) 
we  found  that  changing  the  distance  between  the  plates,  or  the 
area  of  the  plates  immersed,  had  no  effect  on  the  current  sent 
through  a  high-resistance  coil.  Try  the  same  experiment  with 
a  low-resistance  coil  in  the  following  way. 

(a)  Connect  the  improvised  Daniell  cell  with  the  single  turn 
of  coarse  copper  wire  which  connects  the  middle  binding  posts 
of  the  galvanoscope,  and  observe  the  deflection  of  the  compass 
needle. 

(b)  Lift  the  zinc  gradually  out  of  the  cup,  and  record  the 
effect.     Since,  as  proved  in  Experiment  31,  the  E.M.F.  is  not 
diminished  by  decreasing  the  area  of  plates  immersed,  what  do 
you  conclude,  from  Ohm's  law,  must  have  changed  in  the  cir- 
cuit as  the   zinc  was  lifted?    How,  then,  is  the  internal  resist- 
ance affected  by  the  size  of  the  plates  and  the  distance  between 
them? 


98  LABORATORY  PHYSICS 

II.  Current  furnished  by  combinations  of  cells  when  the  exter- 
nal resistance  is  small,  (a)  Connect  a  single  Daniell  cell  with 
the  single-turn  coil  of  the  galvanoscope.  Slip  the  compass  along 
until  the  deflection  is  from  6°  to  10°. 

(b)  Select  another  Daniell  cell  which  gives  approximately 
the  same  deflection  when  tested  in  the  same  way.  Connect  the 
two  cells  in  series.  How  does  the  deflection  given  by  two 
Daniell  cells  joined  in  series  with  a  small  external  resistance 
compare  with  that  given  by  a  single  cell  joined  to  the  same  ex- 
ternal resistance  ?  What  difference  do  you  notice  between  the 
effects  here  obtained  and  those  produced  in  Experiment  31, 
where  the  external  resistance  was  large? 

(<?)  Connect  the  cells  in  parallel  and  observe  the  deflection. 
Since  in  Experiment  31  we  showed  that  the  E.M.F.  is  not 
changed  by  connecting  cells  in  parallel,  how  do  you  explain  the 
observed  effect? 

.III.  Measurement  of  the  internal  resistance  of  Daniell  cells, 
(a)  Join  one  terminal  of  an  improvised  Daniell  cell  to  the  one- 
turn  coil  of  the  galvanoscope,  and  from  the  second  binding 
post  of  this  coil  run  a  short  wire  to  some  fixed  binding  post,  — 
for  example,  one  of  the  posts  of  the  Wheatstone's  bridge.  Join 
the  other  terminal  of  the  cell  to  about  a  meter  of  No.  24  copper 
wire,  to  the  remote  end  of  which  has  been  attached  about  a 
meter  of  No.  36  bare  German  silver  wire.  First  press  the  copper 
wire  hard  against  the  fixed  binding  post  and  place  the  compass 
so  that  the  deflection  is  from  12°  to  20°.  This  deflection  repre- 
sents the  current  which  the  cell  is  able  to  furnish  when  there 
is  no  appreciable  resistance  in  the  circuit  except  the  internal 
resistance  of  the  cell.  Now  take  a  half  turn  of  the  No.  36  wire 
about  the  screw  of  the  fixed  binding  post  and  draw  the  copper 
wire  away  so  as  to  include  a  larger  and  longer  amount  of  the 
No.  36  wire  in  the  circuit.  When  the  current  has  been  reduced 
in  this  way  to  exactly  one  half  its  former  value,  measure  the 


ELECTROLYSIS  AND  THE  STORAGE  BATTERY   99 

length  of  the  German  silver  wire  which  has  been  introduced. 
Since  the  E.M.F.  of  the  cell  has  remained  the  same  while  the 
current  has  been  reduced  to  one  half  its  former  value,  we  know 
that  the  total  resistance  of  the  circuit  must  have  been  doubled. 
Hence,  since  the  resistance  of  the  copper  wire  is  negligible,  the 
internal  resistance  of  the  cell  must  be  just  equal  to  the  resist- 
ance of  the  German  silver  wire  which  has  been  inserted. 

(b)  In  the  same  way  find  the  internal  resistance  of  the  second 
cell  in  terms  of  the  resistance  of  a  length  of  German  silver  wire. 

(c)  In  the  same  way  measure  the  internal  resistance  of  the  two 
cells  joined  in  series.     State  what  relation  exists  between  the 
internal  resistance  of  a  single  cell  and  that  of  two  cells  joined 
in  series. 

(d)  Connect  the  two  cells  in  parallel,  and  obtain  in  the  same 
way  the  joint  internal  resistance  in  terms  of  a  length  of  German 
silver  wire.    What  relation  do  you  find  to  exist  between  the 
resistance  of  a  single  cell  and  that  of  the  two  joined  in  this  way? 
How  should  cells  be  connected  in  order  to  get  as  large  a  current 
as  possible  if  the  external  resistance  is  small  ?  if  the  external 
resistance  is  large? 

All  of  the  above  resistances  may  be  reduced  to  ohms,  if  desired, 
by  taking  into  account  the  fact  that  No.  36  German  silver  wire 
has  a  resistance  of  26  ohms  per  meter  (see  Appendix  B). 


EXPERIMENT  35 
ELECTROLYSIS   AND   THE  STORAGE   BATTERY 

I.  Electrolysis  of  water.  Bare  the  ends  of  two  pieces  of 
copper  wire  and  wrap  each  about, the  head  of  a  wire  nail.1  Con-^ 
nect  the  other  ends  of  the  wires  to  the  terminals  of  two  dry  cells 

1  Platinum  electrodes  are  better,  but  they  are  less  convenient  and  much  more 
expensive. 


100  LABORATORY  PHYSICS 

joined  in  series.  Dip  the  ends  of  the  nails  into  a  dilute  solution 
of  sulphuric  acid  like  that  used  in  Experiment  28.  Is  the  nail 
from  which  the  bubbles  appear  first  and  most  abundantly  con- 
nected to  the  +  or  to  the  —  pole  of  the  battery,  i.e.  to  the  carbon 
or  to  the  zinc  ?  This  gas,  which  is  given  off  most  abundantly,  is 
hydrogen ;  that  which  appears  at  the  other  nail  is  oxygen.  In 
order  to  account  for  these  effects,  we  assume  that  when  the  mole- 
cules of  sulphuric  acid  (H2SO4)  go  into  solution  in  water  they  split 
up  into  two  electrically  charged  atoms,  or  ions,  of  hydrogen  and 
one  oppositely  charged  ion  of  SO4.  It  was  this  hydrogen  which, 
according  to  this  hypothesis,  appeared  at  one  nail  while  the  SO4 
went  to  the  other  and  there  gave  up  an  atom  of  oxygen.  If  this 
hypothesis  is  correct,  must  the  hydrogen  atom  in  solution  carry 
a  -f-  or  a  —  charge  in  order  to  appear  upon  the  nail  upon  which 
you  observed  it  ?  What  kind  of  a  charge  must  the  SO4  ion  carry? 

II.  Electroplating.    Remove  the  nails  and  attach  each  bare 
wire  to  some  sort  of  an  improvised  metal  clip  (ordinary  paper 
fasteners  are  excellent).    In  each  of  these  clips  place  a  nickel 
and  dip  the  lower  half  of  each  into  a  solution  of  copper  sulphate 
(CuSO4).    About  which  nickel  do  you  now  see  bubbles,  the  one 
connected  to  the  +  or  the  one  connected  to  the  —  pole  of  the 
battery?  (The  former  is  called  the  anode,  the  latter  the  cathode.) 
These  bubbles  are  oxygen.    After  about  a  minute  remove  the 
nickels  and  dry  them  with  a  cloth.     Record  what  has  happened. 
Decide  from  your  results  whether  the  copper  ions  of  the  copper- 
sulphate  solution  carry  +  or  —  charges. 

Interchange  the  nickels  between  the  two  clips  and  repeat  the 
above  operations.  Record  the  results.  (If  you  wish  to  restore 
your  nickels  quickly  to  their  original  condition,  dip  them  for  an 
instant  in  strong  nitric  acid  and  rub  with  an  old  cloth.) 

III.  The  storage  battery.1    Arrange  a  simple  cell  in  the  man- 
ner shown  in  Fig.  56,  a  and  b  being  the  copper  and  zinc  strips 

1  Two  sets  of  students  are  expected  to  work  together  on  this  experiment. 


ELECTROLYSIS  AND  THE  STORAGE  BATTERY     101 

to  which  are  connected  the  terminals  of  an  improvised  voltmeter 
consisting  of  the  1000-ohm  resistance  coil  R  and  the  galvano- 
scope  F,  with  the  compass  beneath  its  high-resistance  coil.  A  is 
an  improvised  ammeter  consisting  of  another  gal vanoscope  with 
the  compass  beneath  the  25-turn  coil  of  coarse  wire  ;  r  is  a  resist- 
ance of  about  100  ohms  (use  for  it  the  100-turn  coil  of  No.  40 
wire  of  the  same  galvanoscope  used  for  A) ;  B  is  a  battery  of 
two  dry  cells  connected  in  series  but  not  joined,  at  first,  to  the 
terminals  m  and  n  of  the  cell  circuit.  Move  the  compass  of  F 
until  the  deflection  is  8°  or  10°.  This  amount  of  deflection  then 
represents  the  E.M.F.  of  a 
copper-zinc-sulphuric-acid  cell, 
viz.  approximately  1  volt. 

Now  replace  the  zinc  and 
copper  strips  by  two  strips  of 
sheet  lead.  Does  the  voltmeter 
V  now  indicate  any  E.M.F.? 
Explain  the  reason.  Next  con- 

FIG.  5(5 
nect  m  and  n  to  the  terminals 

of  the  dry  battery  B,  and  as  soon  as  the  needles  are  sufficiently 
quiet  record  the  deflections  shown  by  both  A  and  V\  then 
watch  both  needles  carefully  for  about  two  minutes,  and  record 
the  readings,  expressing  the  reading  of  A  simply  in  scale  divi- 
sions, but  that  of  V  in  both  scale  divisions  and  volts. 

Now  short-circuit  the  terminals  o  and  s  of  the  resistance  r  by 
pressing  a  strip  of  metal  against  the  two  binding  posts  o  and  s  or 
by  connecting  them  with  a  copper  wire.  Watch  the  plates  and 
note  the  hydrogen  appearing  in  considerable  quantity  about  the 
cathode,  while  but  little  oxygen  appears  about  the  anode.  After 
the  current  has  been  running  through  the  short  circuit  on  r  for 
about  two  minutes  lift  the  plates  from  the  liquid.  Do  you  see  a 
faint  reddish  deposit  upon  the  anode  where  the  oxygen  would 
naturally  have  appeared  ?  If  not,  let  the  current  run  a  little 


102  LABORATORY  PHYSICS 

longer  and  observe  again.    This  deposit  is  lead  peroxide.    Why, 
then,  did  so  little  oxygen  gas  appear  about  the  anode  ? 

Replace  the  plates  in  the  acid,  take  away  the  shunt  from  os, 
and  record  the  reading  of  V.  By  how  many  volts  is  it  now  larger 
than  it  was  when  m  and  n  were  first  joined  to  I>  ?  Disconnect 
m  and  n  from  2?,  and  observe  how  many  volts  of  E.M.F.  have 
been  developed  between  the  lead  plates.  Now  watch  the  am- 
meter as  you  join  m  and  n  to  each  other.  What  is  the  direction 
of  the  observed  current  with  reference  to  that  which  the  battery 
sent  through  the  ammeter?  Watch  the  voltmeter  and  ammeter 
for  two  minutes  while  the  storage  cell  is  discharging.  In  view 
of  this  back  E.M.F.  which  the  experiment  has  shown  was 
developed  in  the  lead  cell  by  the  deposit  of  lead  peroxide  on 
the  anode,  explain  why  during  the  charging  of  the  storage  cell 
the  voltmeter  deflection  rose,  while  that  of  the  ammeter  fell. 
From  your  experiment,  decide  how  many  volts  are  required  to 
charge  a  storage  cell.1 

EXPERIMENT  36 
INDUCED  CURRENTS 

I.  Induction  of  currents  by  magnets,  (a)  Set  up  the  D' Arson val 
galvanometer  (Fig.  57),  and  insert  in  the  place  provided  for  it 
a  slender  wire  or  broom-corn  pointer  in  the  manner  shown  in 
the  figure.  Short-circuit  a  simple  cell  by  means  of  a  few  feet 
of  copper  wire  ;  then  to  the  galvanometer  terminals  touch  wires 
which  are  connected  to  the  cell  and  note  the  direction  of  deflec- 
tion. (The  object  of  the  short-circuiting  is  to  prevent  a  too  vio- 
lent throw  of  the  coil.)  Record  the  terminal  (right  or  left)  of  the 
galvanometer  at  which  the  current  entered  it  when  the  deflec- 
tion was  in  a  given  direction  (right  or  left).  This  wTill  enable 

1  If  you  wish  to  repeat  the  experiment  with  the  same  lead  plates,  you  should 
first  clean  them  very  thoroughly  with  sandpaper. 


INDUCED  CURRENTS 


103 


you  henceforth  to  know  at  which  terminal  any  current  enters 
your  galvanometer,  as  soon  as  you  observe  the  direction  of  deflec- 
tion. Connect  to  the  galvanometer  a  600-  or  700-turn  coil  A  of 
No.  27  copper  wire.  Take  particular  pains  to  scrape  the  ends 
of  all  wires  which  are  to  be  joined,  and  to  twist  the  scraped  ends 
firmly  together. 

Thrust  the  coil  A  suddenly  over  the  north  pole  of  the  bar 
magnet,  and  note  and  record  the  direction  and  the  approximate 
amount  of  the  deflection  of  the  end  of  the  pointer  attached  to 
the  coil.  A  paper  scale  sup- 
ported between  the  walls  be- 
neath the  pointer  will  enable 
you  to  estimate  amounts. 

(6)  From  the  direction  of 
the  deflection,  determine  the 
direction  of  the  current  in- 
duced in  the  coil  of  wire 
thrust  over  the  pole.  While 
this  induced  current  was 
flowing  did  it  make  the  end  of 
the  coil,  considered  as  a  temporary  magnet  (see  Experiment  30), 
which  was  approaching  the  N  pole  itself  an  N  or  an  S  pole  ? 

(c)  Suddenly  withdraw  the  coil  from  the  magnet.    Note  and 
record  as  before  the  direction  and  amount  of  deflection.    How 
does  the  direction  and  amount  of  the  induced  current  now  com- 
pare with  that  found  in  (a)  ?    Is  the  end  of  the  coil  which  leaves 
the  magnet  last  of  the  same  sign  as  the  pole  of  the  magnet  or  of 
unlike  sign? 

(d)  Draw  in  your  notebook  four  figures  like  those  shown  in 
Fig.  58,  and  insert  in  each  the  signs  of  the  poles  of  the  coil  due 
to  the  induced  current,  when  the  coil  is  in  the  four  positions 
indicated  in  the  figures  and  moving  in  the  directions  indicated 
by  the  arrows. 


104 


LABOR ATOKY  PHYSICS 


(e)  Repeat  the  same  experiments  with  the  S  pole  of  the  mag- 
net, and  observe  in  each  case  the  direction  of  deflection  and  the 

direction  of  the  current  in- 
duced in  the  coil.  Is  the 
nature  of  the  induced  mag- 
netism of  the  coil  A  in  every 
case  such  as  to  oppose  or  to 
assist  the  motion  of  the  coil  ? 
II.  Induction  of  currents 
by  electro-magnets,  (a)  Slip 
the  700-turn  coil  used  in  I 
over  an  iron  bar  (e.g.  one  of 
the  tripod  rods)  and  connect  it  through  a  commutator  with  a 
battery  B  of  one  or  two  dry  cells,  in  the  manner  shown  in 
Fig.  59.  Place  a  second  similar  coil  over  this  bar  and  connect 
it  with  the  D'Arsonval  galvanometer  as  shown.  Now  make  the 
circuit  by  inserting  the  upper  part  of  the  commutator,  and  record 


Fiu.  5S 


the  effect  produced  upon  the  needle.  From  the  direction  of 
deflection  of  the  pointer,  find  the  direction  in  which  the  current 
flowed  around  the  iron  core  in  the  coil  attached  to  the  galva- 
nometer (the  so-called  secondary}.  Was  the  induced  current  in 
the  same  or  in  the  opposite  direction  to  that  in  which  the  current 


INDUCED  CURRENTS 


105 


from  the  cell  is  circulating  around  the  core  in  the  primary 
coil  ?  What  connection  do  you  find  between  this  experiment 
and  I? 

(b)  Remove  the  commutator  top  and  thus  break  the  circuit  in- 
the  primary.    Note  the  direction  and  amount  of  deflection,  and 
compare  with  that  observed  when  the  current  was  made.    Com- 
pare the  direction  of  the  induced  current  in  the  secondary  with 
that  which  was  flowing  in  the  primary.    Is  the  current  in  the 
secondary  circuit   produced  by  the  magnetism  of  the  electro- 
magnet or  by  changes  in  the  magnetism  of  the  electro-magnet  ? 
Do  -the  induced    currents  in   every  case  tend   to  assist  or  to 
oppose  the  changes  which  are  taking  place  in  the  magnetism 
of  the  core? 

(c)  Push  up  the  base  of  the  tripod  into  contact  with  the  rod 
(Fig.  59),  so  that  the   magnetic  lines  can  have  a  return  iron 
path  instead  of  a  return  air  path. 

Observe  the  amount  of  the  deflec- 
tion at  make  or  break  and  com- 
pare with  the  amount  when  the 
tripod  base  is  removed.  (The  dif- 
ference will  not  be  large,  but  it 
will  be  easily  observable.) 

III.  Principles  of  the  dynamo 
and  motor,  (a)  Hold  the  coil  A 
between  the  poles  of  a  horseshoe 
magnet  (Fig.  60),  and  in  such  a 
position  that  its  plane  is  perpendicular  to  a  line  joining  the 
poles.  Rotate  quickly  through  90°,  i.e.  to  a  position  in  which 
its  plane  is  parallel  to  the  lines  of  force.  Observe  the  direction 
of  deflection  of  the  suspended  coil. 

(b)  After  the  pointer  has  come  to  rest  rotate  the  coil  A  90° 
more,  and  note  and  record  the  direction  of  deflection. 

(c)  Similarly,  rotate  the  coil  through  the  next  two  quadrants. 


106  LABORATORY  PHYSICS 

(d)  If  the  coil  were  to  be  rotated  continuously  in  this  way, 
what  portions  of  the  rotation  would  produce  a  current  in  one 
direction,  and  what  in  the  opposite  direction  ?    In  what  position 
of  the  coil  will  the  induced  current  change  from  one  direction 
to  the  other? 

(e)  In  a  dynamo  a  coil  is  forced  to  rotate  in  the  strong  field 
of  an  electro-magnet  and  induced  currents  are  produced.    In  a 
motor  currents   are  sent  through  a  coil  which  is  in  a  strong 
magnetic  field  and  the  coil  is  forced  to  rotate.    Point  out  the 
parts  of  the  above  apparatus  which  correspond  to  the  dynamo, 
and  those  which  correspond  to  the  motor. 


EXPERIMENT  37 
ELECTRIC   BELLS  AND  MOTORS 

I.  Study  of  electric  bells,  (d)  Connect  an  electric  bell  with 
a  dry  cell,  and  with  an  inexpensive  compass  test  the  condition 
of  the  electro-magnet  first  when  the  clapper  is  held  against  the 
bell,  then  when  it  is  held  away  from  it.  Trace  the  current 
through  the  instrument  and,  with  the  aid  of  a  rough  diagram, 
explain  in  your  notebook  why  the  bell  rings. 

(5)  Connect  a  bell,  two  push  buttons,  and  a  cell  in  such  a  way 
that  pushing  either  button  will  ring  the  bell. 
II.  Study  of  a  small  motor,   (a)  Join  two 
dry  cells  in  series  to  a  small  motor  (Fig.  61). 
As  soon  as  the  motor  begins  to  run  deter- 
mine with  a  small  compass  needle  which 
is  the   N  and  which  the   S  pole   of  the 
field  magnets.    Trace  out  the  winding  of 
the  field  magnet,  and  determine  from  the 
rule  of  Experiment  30  which  pole  should  be  N  and  which  S. 
Do  the  calculated  and  observed  signs  agree? 


SPEED  OF  SOUND  IN  AIR  107 

(b)  Stop  the  motor  and  trace  the  wires  leading  into  one  coil 
of  the  armature.    Find  from  the  rule  what  should  be  the  sign 
of  its  magnetism  at  two  or  three  different  points  in  a  revolu- 
tion.   Test  at  each  point  with  the  compass.    Notice  particularly 
the  points  at  which  its  magnetism  reverses.    Hence,  account 
in  your  notebook  for  the  continuous  rotation  and  for  the  observed 
direction  of  rotation  of  the  motor. 

(c)  From  a  study  of  the  windings,  decide  whether  or  not 
interchanging  the  battery  terminals  would  reverse  the  direction 
in  which  the  motor  runs.    Record  the  answer  in  your  notebook, 
and  then  test  the  correctness  of  your  conclusion  by  experiment. 


EXPERIMENT  38 
SPEED  OF  SOUND  IN  AIR 

A.  Let  the  class  be  divided  into  two  sections  and  placed 
exactly  a  kilometer  apart,  the  distance  being  measured  by  laying 
off  fifty  times  the  length  of  a  cord  20  m.  long.  Each  group 
should  be  provided  with  a  pistol,  blank  cartridges,  and  at  least 
one  stop  watch.  Let  a  member  of  one  group  raise  and  lower 
a  handkerchief  three  times  as  a  ready  signal,  and  simultane- 
ously with  the  last  lowering  let  him  fire  a  pistol.  Let  a  mem- 
ber of  the  other  group  take  with  a  stop  watch  the  time  which 
elapses  between  the  flash  and  the  report  of  the  pistol.  Then 
let  the  operations  at  the  two  stations  be  interchanged,  in  order 
to  eliminate  the  effect  of  any  wind  which  may  be  blowing.  In 
this  way  take  six  or  more  observations,  different  members  of 
the  class  timing  the  interval  in  turn.  Observations  which  differ 
badly  from  the  general  average  and  which  are  evidently  the 
result  of  awkward  handling  of  the  stop  watch  need  not  be 
included  in  the  final  mean.  From  this  mean,  compute  the 
velocity  of  sound  at  the  temperature  of  the  air. 


108  LABORATORY  PHYSICS 

B.1  If  stop  watches  are  not  available,  set  up  a  heavy  pendulum 
which  beats  seconds  ;  attach  some  white  object  to  it ;  set  up 
a  screen  so  that  the  pendulum  can  be  seen  only  when  it  is  pass- 
ing the  middle  point  of  its  swing;  let  one  student  stationed 
near  the  pendulum  pound  loudly  on  some  sonorous  object  at 
each  instant  at  which  the  pendulum  crosses  the  middle  point, 
and  let  the  class  move  away  until  the  beats  of  the  hammer 
appear  again  to  coincide  with  the  passages  of  the  pendulum. 
The  distance  from  the  class  to  the  pendulum  is  obviously  nu- 
merically equal  to  the  velocity  of  sound. 


EXPERIMENT   39 
VIBRATION  NUMBER  OF  A  FORK2 

(a)  Smoke  the  glass  plate  A  (Fig.  62)  by  holding  it  in  the 
flame  of  burning  gum  camphor  or  in  a  gas  flame.3  Keep  the 
plate  moving  back  and  forth  so  that  it  will  not  become  over- 
heated in  one  place  and  crack.  Lay  the  plate  on  the  board, 


FIG.  62 


smoked  side  up,  and  adjust  the  two  styluses  by  means  of  the 
clamps  B  and  C  until  they  touch  the  plate  lightly,  very  near 
each  other  in  the  line  in  which  the  motion  is  to  take  place. 

1  As  in  Experiment  13,  A  and  B  are  intended  as  alternatives,  the  choice 
depending  upon  equipment. 

2  One  "vibration-rate  apparatus"  and  fifteen  glass  plates  will  suffice  for  a 
class  of  thirty.    It  is  recommended  that  the  instructor  make  the  traces,  and 
that  the  students  take  the  measurements. 

8  Instead  of  smoking  the  plate  the  authors  often  mix  up  a  paste  of  whiting  or 
chalk  dust  in  alcohol  and  paint  the  plate  with  it.  This  brings  out  the  trace  as 
well,  and  the  whiting  is  very  much  cleaner  than  lampblack. 


VIBRATION  NUMBER  OF  A  FORK  109 

Set  the  fork  into  vibration  by  striking  it  with  a  wooden  mallet, 
or  bowing  with  a  violin  bow,  and  as  soon  thereafter  as  possible 
start  the  bob  to  vibrating,  and  draw  the  plate  beneath  the  bob 
with  such  rapidity  that  the  trace  of  three  or  four  complete 
vibrations  of  the  bob  will  appear  on  the  plate. 

(b)  Count  the  number  of  vibrations  of  the  fork  corresponding 
to  a  full  vibration  of  the  bob,  i.e.  the  number  of  vibrations  of  the 
fork  between  the  points  A  and  C  (Fig.  63),  then  between  B  and 

'^~^^~^^\C^^~^/^^^ 

•^  J7<         \      7E 

FIG.  63 

I),  then  between  C  and  E,  then  between  D  and  F,  etc.,  estimat- 
ing in  every  case  to  tenths  of  a  vibration.  Take  a  mean  of  these 
counts  as  the  number  of  vibrations  of  the  fork  to  one  of  the  bob. 
(<?)  Repeat  the  observations  on  two  other  traces,  and  take  the 
mean  of  the  three  means  as  the  correct  value  of  the  number  of 
vibrations  of  the  fork  to  one  of  the  bob. 

(d)  Get  the  rate  of  the  bob  by  counting  with  the  aid  of  an 
ordinary  watch  the  number  of  vibrations  which  it  makes  in  one 
or  two  minutes. 

(e)  Compute  the  number  of  full  vibrations  made  by  the  fork 
per  second.    Tabulate  thus : 

First  .Second  Third     Number  vibra- 

trai'c  trace  trace       tions  of  boh 

Vibrations  between  A  and  C  =  .      

Vibrations  between  B  and  D  = 

Vibrations  between  C  and  E  =  

Vibrations  between  D  and  F  =  

Means 

Final  mean  = 

Number  vibrations  of  bob  per  second  = 

.-.  Rate  of  fork  = 


110 


LABORATORY  PHYSICS 


EXPERIMENT  40 


WAVE  LENGTH  OF  A  NOTE  OF  A  TUNING  FORK 

(a)  Let  one  student  strike  a  C'  fork  (i.e.  one  which  makes  512 
vibrations  per  second)  upon  a  block  of  wood,  and  then  quickly 
hold  it  above  the  tube  of  Fig.  (34,  with  the  flat 
face  of  one  prong  just  above  the  end  of  the 
tube.  (Use  the  tube  of  Fig.  11,  p.  14.)  Let 
a  second  student  raise  and  lower  the  vessel 
A  while  the  fork  is  sounding,  and  note  as 
accurately  as  possible  the  shortest  length  of, 
maximum  resonance.  Mark  this  position  by 
means  of  a  small  rubber  band.  Test  the  cor- 
rectness of  the  setting  by  several  observations. 
(b)  Locate  in  the  same  way  a  second  position 
of  resonance  lower  in  the  tube,  and  mark  with 
a  rubber  band  as  above.  Since  the  distance 
between  two  positions  of  maximum  resonance 
is  exactly  one  half  wave  length,  twice  the  distance  between  the 
rubber  bands  will  be  equal  to  the  wave  length  of  the  note  sent 
forth  by  the  sounding  tuning  fork.  Compare  this  value  of  the 
wave  length  with  that  computed  by  dividing  the  speed  of  sound  at 
the  temperature  of  the  room  by  the  vibration  number  of  the  fork 
as  marked  upon  it.  (Speed  of  sound  in  air  at  0°  C.  =  332  m.  per 
second.  It  increases  60  cm.  for  each  degree  rise  in  temperature.) 
(c)  Find,  in  the  same  way  the  wave  length  of  a  fork  one 
octave  lower  than  the  first.  Tabulate  results  thus  : 


First  resonant 

length  h 
Fork  No.  1 
Fork  No.  2 

Number  vibrations  of  fork  No.  1  = 
Number  vibrations  of  fork  No.  2  = 


Second  resonant 
length  l> 


Difference  x  2 
=  X 


.-.  Calculated  wave  length  =  — 
.-.  Calculated  wave  length  =  — 


LAWS  OF  VIBRATING  STRINGS  111 

State  in  notebook  how  you  have  proceeded  to  find  X. 

Show  how  this  method  might  be  used  for  finding  the  velocity 
of  sound. 

Since  the  speed  of  sound  is  the  same  for  notes  of  all  pitches, 
what  conclusion  can  you  draw  from  your  experiment  in  regard 
to  the  vibration  frequencies  of  two  notes  which  are  an  octave 
apart  ? 

EXPERIMENT  41 
LAWS  OF  VIBRATING  STRINGS 

I.  Effect  of  length  on  the  vibration  rate  of  a  stretched  wire. 
(a)  Stretch  a  fine  steel  piano  wire  (No.  00)  along  the  board  A 


A 

FIG.  65 

(Fig.  65),  insert  a  bridge  at  6,  and  hang  a  pail  having  a 
capacity  of  at  least  six  quarts  over  the  pulley  p.  Pour 
water  into  the  pail  until  the  note  given  by  the  wire  (best  ^F^| 

picked  near  the  middle)  is  in  unison  with  the  note  of  the      V ; 

lowest  fork  provided,  viz.  C.    Measure  carefully  the  length  of 
the  wire  between  the  fixed  end  and  b. 

(b)  Move  the  bridge  b  until  the  note  given  by  the  wire  is 
exactly  in  tune  with  a  fork  C',  an  octave  higher  than  the  first 
one.    Measure  and  record  the  length  from  the  fixed  end  to  b. 

(c)  In  the  same  way  (i.e.  by  moving  b)  tune  the  wire  to  uni- 
son with  a  third  fork,  e.g.  G  above  middle  C,  and  measure  and 
record  the  corresponding  length. 

(d)  From  a  study  of  the  measured  lengths  and  of  the  vibra- 
tion numbers  as  marked  on  the  forks,  find  and  state  in  your 
notebook  the  law  connecting  the  rate  of  a  vibrating  string  with 
its  length  when  the  tension  is  kept  constant. 


112  LABORATORY  PHYSICS 

II.  Effect  of  tension  on  the  vibration  rate  of  a  stretched  wire. 
(a)  Set  up  side  by  side  two  boards  like  A  (Fig.  65),  both  of 
which  are  provided  with  No.  00  piano  wire.  Place  the  bridges 
b  at  the  same  distance,  say  60  cm.  from  the  left  end  of  each. 
Produce  the  same  tension  in  the  two  wires  by  hanging  from 
each  a  like  weight,  for  example  a  pail  containing  a  small  amount 
of  water.  The  weights  should  be  of  such  size  as  to  produce 
in  the  plucked  wires  a  low  but  perfectly  distinct  musical  note. 
Bring  the  two  wires  into  exact  unison  by  adjusting  the  water 
in  one  of  the  pails  until  no  beats  are  heard  when  the  strings 
are  sounded  together.  Find  the  exact  tension  on  one  of  the 
wires  by  weighing  the  pail  and  water  carefully  with  a  spring 
balance.  Produce  the  exact  octave  on  the  other  wire  by  moving 
the  bridge  until  the  wire  is  only  one  half  as  long  as  at  first. 
Bring  the  first  wire  into  unison  with  it  by  adding  water  to  the 
pail,  leaving  the  length  exactly  as  at  first.  Weigh  the  pail  and 
water  again,  and  find  the  ratio  of  the  weights  in  the  two  cases. 
In  order  to  double  the  rate,  how  many  times  has  it  been  neces- 
sary to  multiply  the  stretching  force  ? 

(b)  Make  the  second  wire  just  two  thirds  its  original  length, 
its  tension  still  being  kept  constant.  In  what  ratio  will  this 
change  its  vibration  number?  Adjust  the  amount  of  water  in 
the  pail  hanging  from  the  first  wire  until  the  two  are  in  unison, 
and  weigh  on  the  spring  balance  again. 

From  the  law  suggested  in  a,  calculate  what  this  last  stretch- 
ing weight  should  have  been,  and  see  how  well  it  agrees  with 
the  observed  value. 

Tabulate  results  thus : 

I.  Length  of  C  wire  =  -2— k.  cm. 

Length  of  C'  wire  =    *~\  cm. 

Length  of  G  wire  =%&+3cm. 

Calculated  length  of  C'  wire  = cm. 

Calculated  length  of  G  wire    =  —  —  cm. 


REFLECTION  FROM  PLA>'E  MIRRORS 


113 


II.  First  stretching  weight 

Second  stretching  weight  =  I  •**• 

Second  divided  by  first 

Third  stretching  weight  (calculated)  = g. 

Third  stretching  weight  (observed)    = g. 

State  in  notebook  the  laws  discovered  in  I  and  II. 


EXPERIMENT  42 
LAWS  OF  REFLECTION  FROM  PLAXE  MIRRORS 

I.  To  prove  that  angle  of  incidence  equals  angle  of  reflection. 

(a)  Blacken  one  side  of  a  strip  of  plate  glass  or  a  microscope 

slide  ;  attach  it  by  means  of  a       y  . 

rubber  band  to  a  small  wooden 

block,  and  then  set  it  on  edge  so 

that  the  line  AC  (Fig.  66),  drawn 

on  a  sheet  of  paper,  coincides 

with  the  plane  of  the  unblackened 

face.    The  rear  face  is  blackened 

in  order  to  prevent  reflection  from 

that  face  and  enable  one  to  work 

with  the  light  reflected  from  the 

front  face  alone.    Set  a  pin  at  a  point  B  against  the  face  of  the 

glass.    Set  another  pin  at  any  point  P,  and  then,  placing  the  eye 

so  as  to  sight  along  B  and  P",  the  image  of  P,  set  a  third  pin 

P'  somewhere  in  this  line  of  sight.    Remove  the  glass  plate  and 

with  a  protractor  or  a  pair  of  dividers  construct  a  perpendicular 

BE  to  AC  at  the  point  B.    Draw  PB  and  P'B  and  measure  the 

angle  of  incidence  PBE  and  the  angle  of  reflection  P'BE  with  the 

protractor.    If  a  protractor  is  not  at  hand,  draw  an  arc  with  B  as 

center,  cutting  the  lines  PB  and  P'B  at  M  and  0,  and  measure 

the  lines  MN  and  ON. 


114 


LABORATORY   PHYSICS 


(b)  Repeat  ior  some  other  position  of  P. 

(<?)  Finally  set  P  at  such  a  point  that  it  is  directly  in  line  with 
its  own  image  P"  and  B.  Draw  the  line  PB  and  also  construct 
the  perpendicular  to  AC  at  B.  If  the  angle  of  incidence  is  equal 
to  the  angle  of  reflection,  the  two  lines  should  exactly  coincide. 
II.  To  locate  the  image  formed  by  a  plane  mirror,  (a)  Again 
set  up  the  piii  at  P  (Fig.  67),  draw  the  line  AC,  and  place  the 

edge  of  the  mirror  upon 

,,.•$;..  .  it,  then  lay  a  straight- 

/'/' •  \  '.'-.,  edge  on  the  paper  in 

,-''    /    /     \    \  "s  N  successive   positions 

ab,  cd,  ef,  etc.,  such 
that  the  image  P" 
always  appears  to  lie 


in  the  prolongation  of 
the  edge  of  the  ruler. 
Draw  the  correspond- 
ing lines,  ab,  cd,  etc. ;  then  remove  the  glass  and  locate  the 
image  P"  by  prolonging  these  lines  to  their  point  of  intersection. 
(b)  Measure  the  perpendicular  distance  from  P  to  A  C  and  from 
P"  to  AC.    Also  measure  the  angle  which  PP"  makes  with  AC. 
Tabulate  your  results  neatly,  and  state  the  conclusions  which 
you  draw  from  I  and  II. 


EXPERIMENT  43 

TO  FIND   THE    RATIO   OF    THE    VELOCITIES   OF    LIGHT    IN 
AIR  AND  GLASS 

(Index  of  refraction  of  glass) 

Draw  a  straight  line  AC  (Fig.  68)  across  a  large  sheet  of 
paper,  and  set  one  edge  of  the  plate-glass  prism  mnO  in  exact 
coincidence  with  it.  Lay  a  ruler  on  the  paper  in  such  a  position 


INDEX  OF  REFRACTION  OF  GLASS  •  115 

that,  as  you  sight  along  its  edge  from  some  position  E  in  the 
plane  wwO,  the  apex  0  of  the  prism,  as  seen  in  the  face  wn, 
appears  to  lie  in  the  prolongation  of  the  edge  of  the  ruler. 
Draw  a  fine  line  ab  along  this  edge.  Then  move  the  eye  to  a 
position  E',  about  as  far  to  the  right  as  E  was  to  the  left  of  the 
normal  to  wn,  and  draw  in  the  same  way  a  line  cd.  Mark  the 
position  of  0  carefully  by  means  of  a  pin  prick.  Then  remove 
the  prism,  and  with  an  accurate 
straightedge  and  a  very  sharp 
pencil  or  knife  edge  prolong  ab 
and  cd  until  they  meet  in  some 
point  0'.  The  point  0  is  then  the 
center  in  the  glass  of  the  light 
waves  by  means  of  which  you  see 
the  apex  0,  while  the  point  0'  is 
the  center  of  the  same  waves  after 
they  have  emerged  into  air.  If, 
therefore,  from  Oand  O'as  centers, 
the  two  arcs  qrt  and  qr't  are  con- 
structed, the  arc  qrt  would  repre- 
sent the  shape  and  position  of 
the  wave  from  0  when  it  has  ^  „  fla 

J:  IG.  Do 

reached  the  points  q  and  t,  if  the 

speed  in  air  were  the  same  as  the  speed  in  glass,  while  qr't  is 
the  actual  position  of  this  wave  in  view  of  the  fact  that  light 
travels  faster  in  air  than  in  glass,  sr'/sr  is  then  the  ratio  of  these 
two  speeds.  But  sr'/sr  is  also  the  ratio  of  the  curvatures  of 
the  arcs  qr't  and  qrt,  i.e.  it  is  the  ratio  of  the  amounts  by  which 
these  curved  lines  depart  from  the  straight  line  qst.  Now  if,  at 
a  given  point,  one  arc  is  curving  twice  as  rapidly  as  another,  it 
is  evident  that  its  center  can  be  but  half  as  far  away,  i.e.  the 
curvatures  of  two  arcs  are  always  inversely  proportional  to 
their  radii.  Hence  the  ratio  sr'/sr  is  the  same  as  the  ratio  Oq/0'q. 


116  LABORATORY  PHYSICS 

Measure  these  distances  as  carefully  as  possible  with  a  meter 
stick,  and  record  your  value  for  the  ratio  of  the  velocities  of 
light  in  air  and  glass.  This  is  called  the  index  of  refraction 
of  glass.  Repeat  the  observations,  using  different  positions  of 
E  and  E',  and  see  how  well  the  two  observations  agree. 
Record  your  results  as  follows  : 

First  trial  Second  trial 

Oq       -—  .  Oq 

O'q  O'q 

Index  =  Index  =  - 

Per  cent  of  difference  between  first  and  second  =  — 
Mean  value  of  index 

EXPERIMENT  44 
THE   CRITICAL  ANGLE  OF   GLASS 

Place  the  plate-glass  prism  ABC  (Fig.  69),  having  three  polished 
faces,  upon  a  large  sheet  of  paper  in  front  of  a  window  OR 
through  which  the  sky  is  visible.  If  desired,  OR  may  be  a  piece 
of  ground  glass  behind  which  a  white  light  is  placed.  Place  the 
eye  in  a  position  E,  so  as  to  observe  the  image  of  the  sky  or 
ground  glass  as  it  is  seen  by  reflection  from  AB.  A  bluish- 
green  line  will  be  seen  dividing  AB  into  two  parts  of  markedly 
different  brightness. 

The  part  to  the  right  is  brighter  than  the  part  to  the  left. 
If  this  line  dividing  the  field  is  not  seen  at  first,  it  will  appear 
on  moving  the  eye  to  the  left  or  right.  Move  the  eye  about 
until  the  green  edge  of  this  line  is  brought  into  exact  coinci- 
dence with  a  small  ink  spot  placed  at  s  on  the  face  AB.  From- 
the  figure,  it  will  appear  that  the  light  which  comes  to  the  eye 
by  reflection  from  the  various  points  along  AB  must  make  a 
larger  and  larger  angle  of  incidence  on  AB  as  the  point  con- 
sidered lies  farther  and  farther  to  the  right  of  A.  When  this 


THE  CRITICAL  ANGLE  OF  GLASS  117 

angle  is  equal  to  or  greater  than  the  critical  angle,  as  is  the 
case  between  s  and  B,  the  whole  of  the  light  incident  upon  AB  is 
reflected ;  when  it  is  less  than  the  critical  angle,  as  is  the  case 
between  A  and  s,  part  is  reflected  and  part  transmitted^  The 
blue-green  line  which  separates  the  field  into  parts  of  unequal 
brightness  represents  the  position  on  AB  at  which  total  reflec- 
tion begins,  i.e.  the  angle  i  is  the  critical  angle  for  glass.  To 
measure  this  angle,  lay  a  ruler  so  that  its  edge  appears  to  lie  in 
the  same  straight  line  with  the  point  s  and  the  green  edge  of  the 


line  in  the  field,  and  mark  with  a  line  on  the  paper  the  position 
of  the  straightedge.  Then  with  a  sharp  pencil  or  a  knife  draw 
an  outline  ABC  of  the  prism  upon  the  paper,  and  place  a  pin 
prick  at  s  just  beneath  the  ink  spot  s  on  the  face  AB.  Remove 
the  prism  and  extend  the  line  just  drawn  until  it  meets  AC  at 
some  point  n.  Connect  this  point  n  with  the  pin  prick  at ,«, 
erect  the  perpendicular  upon  AB  at  *,  and  measure  with  the  . 
protractor  the  angle  i.  This  is  the  critical  angle  for  glass. 

Extend  the  lines  »n  and  the  perpendicular  at  s  so  as  to  make 
them  from  6  in.  to  1  ft.  in  length.    Draw  uv  parallel  to  AB. 


118  LABORATORY  PHYSICS 

Then  us/uv  should  give  the  same  value  for  the  index  of 
refraction  as  that  obtained  in  the  last  experiment.  The  proof 
of  this  statement  is  not  suitable  for  an  elementary  text,  but 
the  measurement  will  furnish  an  interesting  check  as  to  the 
accuracy  of  the  results  of  the  experiment. 


EXPERIMENT  45 
FOCAL  LENGTH   OF  A  CONCAVE  MIRROR 

I.  Support  the  concave  mirror  by  means  of  a  clamp  in  dii 
sunlight,  and  let  the  image  of  the  sun  be  thrown  upon  a  narro\ 
strip  of  paper  held  in  front  of  the  mirror.    Measure  the  distance 
from  the  mirror  to  the  point  at  which  the  spot  of  light  on  the 
thin  strip  is  smallest  and  brightest.    This  distance  is  the  focal 
length.    Designate  it  by  the  letter/. 

II.  Throw  the  image  of  a  distant  house  on  the  thin  strip  of 
paper  in  the  same  way.    Repeat  the  above  measurement. 

III.  Place  a  candle  flame  or  an  electric  light  about  25  cm.  or 
30  cm.  from  the  mirror  and  locate  the  position  of  the  image  by 
letting  it  fall  on  the  narrow  screen.    Compute  the  focal  length 
from  the  formula 

'  -+i=4' 

u      v     f 

in  which  u  and  v  are  the  distances  of  the  object  and  image 
respectively  from  the  center  of  the  mirror. 

IV.  Set  up  a  pin  on  a  block  so  that  its  head  is  about  oppo- 
site the  middle  of  the  mirror.    Move  the  pin  out  to  about  twice 
the  focal  distance  from  the  mirror.    If  the  eye  is  placed  in  front 
of  the  mirror  and  as  much  as  8  in.  or  10  in.  farther  from  it  than 
the  pin,  the  object  and  image   may  both  be  seen,  the   image 
inverted  and  the  object  erect  in  the  manner  shown  in  another 
connection  in  Fig.  71.    Shift  the  position  of  the  pin  or  of  the 


THE  CONVEX  LENS  119 

mirror  until  the  image  of  the  head  of  the  pin  is  exactly  in  line 
with  the  head  of  the  pin  itself.  Move  the  eye  to  right  and  left 
and  see  whether  there  is  any  relative  motion  of  the  pin -and  its 
image.  If  so,  it  is  because  they  are  not  the  same  distance  from 
the  eye.  The  one  which  is  farther  away  will  move  to  the  left 
when  the  eye  is  moved  to  the  left,  and  to  the  right  when  the 
eye  is  moved  to  the  right.  (Test  the  correctness  of  the  above 
statement  by  holding  two  pencils  in  line,  but  at  different  dis- 
tances from  the  eye,  and  noticing  how  they  appear  to  move  with 
reference  to  each  other  as  the  eye  is  moved  from  side  to  side.) 
Adjust  the  position  of  the  pin  until  there  is  no  relative  motion 
between  the  pin  and  its  image  as  the  eye  is  moved  from  side 
to  side.  The  image  of  the  pin  is  now  at  the  same  plape  as  the 
pin  itself,  hence  the  pin  must  be  at  the  center  of  curvature  of 
the  mirror.  Measure  the  distance  from  pin  to  mirror.  This 
distance  is  the  radius  of  curvature  of  the  mirror.  Find  what 
relation  exists  between  this  distance  and  the  focal  length  of 
the  mirror. 

Record  results  as  follows : 

Focal  length,  by  I    = Focal  length,  by  III  = 

Focal  length,  by  II  = \  radius  of  mirror      = 


EXPERIMENT   46 
LAWS  OF  IMAGE  FORMATION  IN  CONVEX  LENSES 

I.  Set  up  in  the  positions  shown  in  Fig.  70  a  wire  netting  0, 
a  reading  glass  L  of  about  15  cm.  focus,  and  a  block  B  pro- 
vided with  a  paper  scale  s.  Set  a  gas  flame  behind  0  to  insure 
bright  illumination.  Adjust  B  and  L  until  the  image  of  the 
netting  is  sharply  outlined  on  «.  Then  measure  w,  the  distance 
from  0  to  the  middle  of  the  lens  Z,  and  v,  the  distance  from  L 
to  *;  Next  read  on  «  the  number  of  millimeters  covered  by  ten 


120 


LABORATORY  PHYSICS 


or  twenty  squares  in  the  image  of  the  netting.    Then  with 


another  scale  measure  the  number  of 
by  the  same  number  of  squares  on 
two  observations  give  respectively 
image  and  the  length  L  of  the  ob- 


millimeters  covered 
the  netting  0.  These 
the  length  L'  of  the 
ject.  Repeat  the  same 


observations  with  three  or  four  different  values  of  w,  such  as 
30  cm.,  40  cm.,  50  cm.,  and  60  cm.,  and  calculate  the  focal 
length  /  of  the  lens  from  the  formula 


M-l 

U         V          f 


Also  take  the  ratios  L/L'  and  u/v  and  tabulate  as  follows  : 


What  conclusion  do  you  draw  from  the  last  two  columns? 
II.    Find  the  focal  length  of  the  lens  directly  by  removing 
0  and  casting  the  image  of  a  distant  chimney  or  house  upon  s. 


MAGNIFYING  POWEK  OF  A  SIMPLE  LENS       121 


FIG.  71 


III.  As  a  final  check  on  the  focal  length,  place  a  plane 
mirror  behind  the  lens  and  mount  a  pin  in  front  of  the  lens 
opposite  its  center.  Adjust  the 
pin  by  the  method  of  parallax 
(the  method  used  in  IV,  Experi- 
ment 45)  until  the  image  of  the 
head  of  the  pin  coincides  with 
the  head  of  the  pin  itself.  The 
distance  from  the  pin  to  the  center 
of  the  lens  must  then  be  equal  to 
the  focal  length  of  the  lens,  as  is  shown  by  the  diagram  (Fig.  71), 
since  the  waves  between  the  lens  and  the  mirror  are  plane. 

Compare  the  results  of  II  and  III  with  the  fourth  column 
above. 

EXPERIMENT  47 
MAGNIFf  ING  POWER  OF  A  SIMPLE  LENS 

Fig.  7  2  shows  a  so-called  linen  tester,  —  a  simple  lens  at  the 
focus  of  which  is  a  square  hole  in  a  brass 
frame.  Lay  one  meter  stick  on  the  table 
(see  the  figure),  and  with  the  aid  of 
another  one  held  vertically,  adjust  the 
position  of  the  eye  which  is  viewing  the 
horizontal  stick  so  that  the  distance  from 
the  stick  to  the  eye  is  just  25  cm.  Then, 
keeping  the  head  always  in  this  position, 
bring  up  the  lens  as  close  as  possible  to 
23  the  other  eye.  Keep  both  eyes  open  at 
the  same  time  and  observe  how  many  mil- 
limeters on  the  stick  seen  with  one  eye 

are  covered  by  the  hole  seen  through  the  lens  with  the  other 
eye.    Divide  the  number  by  the  measured  width  of  the  hole  in 


FIG.  72 


122 


LABORATORY  PHYSICS 


millimeters.  This  is  obviously  the  magnifying  power  of  the 
simple  lens,  since  it  shows  how  many  times  larger  the  object 
appears  when  seen  through  the  lens  than  when  viewed  with 
the  naked  eye  at  the  distance  of  most  distinct  vision,  viz.  25  cm. 
Measure  as  accurately  as  possible  the  focal  length  /  of  the  lens, 
i.e.  the  distance  from  the  middle  of  the  lens  to  the  hole,  and 
see  how  well  the  observed  magnifying  power  agrees  with  the 
theoretical  value,  viz.  25//. 


EXPERIMENT  48 
THE  ASTRONOMICAL  TELESCOPE 

1.  To  construct   a  telescope.    With  the   simple   magnifying 
glass  used  in  the  last  experiment,  and  an  objective  consisting 

of  the  reading  glass  of 
Experiment  46,  con- 
struct an  astronomical 
telescope  as  follows. 
Set  the  reading  glass 
in  some  support  (Fig. 
73)  and  find,  with  the 
aid  of  a  piece  of  white 
cardboard,  the  dis- 
tance from  the  lens 
at  which  the  image  of 
a  distant  building  or 
window  is  formed.  Then  set  up  the  linen  tester  behind  the 
card  at  its  focal  length  from  it.  Now  remove  the  card  and  view 
the  image  of  the  distant  object  through  the  eyepiece.  Slide  the 
eyepiece  support,  if  necessary,  until  the  distant  object,  prefer- 
ably a  brick  wall,  is  very  sharply  seen ;  then  measure  the  dis- 
tance between  the  lenses  and  compare  this  distance  with  the  sum 


FIG.  73 


THE  COMPOUND  MICROSCOPE  123 

of  the  focal  lengths.  Do  you  find  any  simple  relation  between 
these  quantities  ?  Can  you  see  any  reason  why  there  should  be 
some  such  relation  ?  Explain. 

II.  To  measure  the  magnifying  power  of  the  telescope. 
Focus  the  telescope  upon  two  heavy  horizontal  marks  drawn, 
for  example,  on  a  blackboard  on  the  opposite  side  of  the  room. 
Let  the  lines  be  from  3  in.  to  6  in.  apart.  When  the  lenses  have 
been  adjusted  so  that  a  distinct  image  of  the  marks  is  seen  with 
the  eye  which  is  looking  through  the  telescope,  open  the  other 
eye  and  direct  another  student  to  make  marks  on  the  board 
which  shall  coincide  with  the  apparent  positions  on  the  board 
of  the  images  of  the  two  marks  as  seen  through  the  telescope. 
It  may  be  found  difficult  at  first  to  give  attention  to  both  eyes 
at  once,  but  a  little  practice  will  make  it  easy.  Repeat  several 
times  and  compute  the  magnifying  power  from  each  observation. 
Compare  this  magnifying  power  with  the  theoretical  value  for 
the  magnifying  power  of  a  telescope,  i.e.  the  ratio  of  the  focal 
lengths  of  the  objective  and  eyepiece.  (These  were  found  in 
Experiments  46  and  47.) 


EXPERIMENT  49 
THE  COMPOUND  MICROSCOPE 

I.  To  construct  a  microscope.  Place  two  corks  which  con- 
tain holes  about  1  cm.  in  diameter  in  the  ends  of  a  cardboard 
or  tin  tube  4  in.  or  5  in.  long,  and  with  the  aid  of  a  rubber 
band  fix  the  lenses  of  two  of  the  linen  testers  over  the  holes, 
(Fig.  74).  Support  the  tube  vertically  over  the  table  by  means 
of  clamps,  and  raise  or  lower  it  until  a  magnified  image  of  a 
millimeter  scale  lying  on  a  block  beneath  it  is  in  sharp  focus, 
the  distance  from  the  table  to  the  top  of  the  tube  being  some- 
what more  than  25  cm. 


124 


LABOKATOKY  PHYSICS 


II.  To  determine  its  magnifying  power.  Lay  a  meter  stick 
on  the  table,  as  in  Fig.  74,  and  elevate  one  end  of  it  until  the 
distance  from  the  eye  which  is  not 
looking  through  the  microscope  to 
,  the  stick  is  exactly  25  cm.  By  fix- 
ing the  attention  simultaneously  on 
the  two  scales  seen,  one  through  the 
microscope  and  the  other  with  the 
unaided  eye,  determine  how  many 
millimeters  on  the  meter  stick  are 
covered  by  1  mm.  of  the  scale  seen 
in  the  microscope,  i.e.  find  the  num- 
ber of  "  diameters  "  of  magnifica- 
tion of  the  microscope.  If  ?:  is  the 
distance  from  the  objective  to  the 
focal  plane  of  the  eyepiece,  i.e.  the  distance  between  the  centers 
of  the  lenses  minus  the  focal  length  /  of  the  eyepiece,  and  if  lz 
represents  the  distance  from  the  objective  to  the  object  viewed, 
then  Zj/^  represents  how  many  times  the  image  formed  by  the 
objective  is  larger  than  the  object.  Since  the  eyepiece  magni- 
fies this  image  25//1  times,  the  total  magnifying  power  of  the 
compound  microscope  should  be  25/fx  li/lz.  Measure  ^  and 
/2  and  compare  the  observed  value  with  this  calculated  value, 
and  tabulate  the  results  in  neat  form. 


FIG.  74 


EXPERIMENT  50 
PRISMS 

I.  Path  of  a  beam  of  light  through  a  prism.  Draw  a  line  AC 
(Fig.  75)  on  a  page  of  your  notebook.  Place  the  prism  on  the 
paper  in  the  position  indicated  in  the  figure.  Light  coming  to 
the  prism  in  the  direction  AC  will  be  bent  both  upon  entering 
and  leaving  the  prism.  Place  a  straightedge  on  the  paper  and 


PRISMS  125 

adjust  it  carefully  until  it  is  exactly  in  line  with  the  apparent 
direction  of  AC  as  seen  through  the  prism.  With  a  sharp  pencil 
draw  a  line  DE  along  the  edge  of  the  ruler,  and  trace  the  out- 
line of  the  prism  on  the  paper.  Remove  the  prism  and  extend 
the  lines  AC  and  DE  until  they 
meet,  at  /  and  g,  the  lines  which  rep- 
resent the  prism  faces.  Then  AfgE 
will  be  the  path  of  the  light  which  A, 
traverses  the  prism. 

II.   Dispersion,    (a)  With  the  aid  ~ ~ 

of  the  knowledge  gained  in  I,  place 

the  prism  in  direct  sunlight  in  such  a  way  that  the  beam  from 
the  sun  is  thrown  upon  some  shaded  portion  of  the  floor.  Place 
between  the  prism  and  the  sun  a  sheet  of  cardboard  containing  a 
horizontal  slit  2  mm.  or  3  mm.  wide.  Name  the  colors  which  you 
see  upon  the  floor  and  into  which  the  sunlight  has  been  resolved. 
Which  has  suffered  the  largest  bending  in  passing  through  the 
prism,  and  which  the  smallest?  Cut  two  2-mm.  slits  in  the 
cardboard,  and  leave  a  2-mm.  space  between  them.  Cover  one 
slit  and  note  the  spectrum ;  then  uncover  and  note  the  change 
in  color  in  the  middle  of  the  patch  where  the  two  spectra  over- 
lap. Does  this  show  that  the  spectral  colors  may  be  recombined 
into  white  light?  Hold  the  prism  alone  without  any  slit  in  the 
sunlight.  Explain  now  why  only  the  edges  of  the  patch  appear 
colored,  while  the  middle  appears  uncolored. 

(b)  Now  place  the  prism  immediately  before  the  eye  in  such  a 
way  that  you  can  observe  through  it  a  narrow  (2-mm.)  strip  of 
white  paper  placed  on  a  black  background,  or  better  still,  an 
electric-lamp  filament,  or  the  narrow  edge  of  a  gas  flame.  Explain 
why  the  red  now  appears  to  be  on  the  side  next  the  base  of  the 
prism,  while  the  blue  is  nearer  the  apex.  Substitute  a  broad 
sheet  of  paper  for  the  narrow  strip.  When  viewed  through  the 
prism,  one  edge  will  appear  red  shading  into  yellow  on  the  inner 


126 


LABORATORY  PHYSICS 


side,  and  the  other  will  appear  blue  shading  into  green.    Explain 
why  the  paper  does  not  appear  colored  in  the  middle,  while  it 

does   appear   colored   at   the 
edges.    Explain  further  why 
E    the  two  edges  are  differently 
colored. 

III.  Bright-line  spectra. 
Let  one  student  hold  succes- 
sively in  a  Bunsen  flame  ar- 
ranged as  in  Fig.  76  platinum 
wires,  or  bits  of  asbestus,  which  have  been  dipped,  one  in  a 
solution  of  common  salt  (sodium  choride),  another  in  lithium 
chloride,  and  another  in  calcium  chloride,  taking  care  that  the 
wire  itself  is  kept  below  the  lower  edge  of  the  slit  «.  Let 
other  students  observe  through  the  prisms  at  distances  of  about 
10  ft.,  in  the  manner  indicated  in  the  figure,  and  record  the 
character  of  the  spectra  which  the  incandescent  vapors  of  these 
substances  give  rise  to. 

IV.  Path  of  a  beam  of  light  through  a  plate  of  glass  with 
parallel  faces,  (a)  Place  two  prisms  together  in  the  manner 
shown  in  Fig.  77,  thus  forming  in  effect  a  single  piece  of  glass 
with  the  parallel  edges  om  taidpn.  Draw  a  heavy  line  AB,  then 
place  a  straightedge  in  line 
with  the  image  of  this  line, 
and  draw  a  mark^'.B'  along  its 
edge  showing  the  direction  of 
the  light  after  passing  through 
the  parallel  faces  om  and  pn. 
From  the  result  obtained,  state 
what  happens  to  the  direction  of  a  ray  of  light  which  passes 
through  a  plate  of  glass  with  parallel  faces. 

(A)  Hold  one  prism  firmly  in  place  and  slide  the  other  along 
the  common  face  until  the  effective  thickness  of  glass  between 


FIG.  77 


PRISMS 


127 


the  faces  mo  and  pn  is  only  one  half  as  much  as  before,  i.e. 
until  the  vertex  of  one  prism  falls  at  the  middle  of  one  side  of 

the  other,  as  shown  in  Fig.  78.    With  jH 

the  same  line  AE  and  the  face  om  ex- 
actly parallel  to  its  initial  position,  draw 
again  a  line  A'B'  in  the  apparent  pro- 
longation of  AB. 

(c]  Slide  the  prisms  into  the  position 
shown  in  Fig.  79,  being  very  careful  to 
keep  the  face  om  parallel  to  its  initial 
direction.  The  thickness  of  glass  to  be 


FIG.  78 


FIG.  79 


traversed  will  now  be  three 
times  as  great  as  in  (b).  Pro- 
ceed precisely  as  above. 

(d)  Remove  the  prisms  and 
prolong  AB.  Measure  the  per- 
pendicular distances  between 
AB  and  the  three  prolonga- 
tions of  AB  as  seen  through 
the  three  thicknesses  of  glass. 
State  in  what  way  the  experiment  shows  that  the  lateral  dis- 
placement of  the  beam  varies  with  the  thickness  of  the  glass. 

(e)  If  the  prisms  are  so  placed  that  AB  is  perpendicular  to  the 
face  om  (Fig.  80),  no  trace  of  the  line  can 
be  seen  at  A'B'.  But  if  a  drop  of  water  is 
placed  between  the  faces  in  contact  along 
mp,  the  line  AB  can  be  seen  very  plainly 
at  A'B1.  Explain. 

If  now  A'B'  is  drawn  as  above  and  if 
AB  is  exactly  perpendicular  to  om,  then  on  removing  the  prisms 
and  extending  AB  it  will  be  found  that  AB  and  A'B'  lie  on  the 
same  straight  line,  i.e.  there  has  been  no  lateral  displacement. 
Why? 


128  LABORATORY  PHYSICS 

EXPERIMENT  51 1 
PHOTOMETRY 

I.  Law  of  inverse  squares.    Set  up  a  paper  screen  with  an 
oiled  spot  in  the  middle  between  a  single  candle  on  one  side 
and  a  group  of  four  candles  on  the  other.    See  that  the  flames 
of  the  five  candles  are  as  nearly  as  possible  of  equal  height ;  then 
move  the  screen  back  and  forth  until  a  position  is  found  in 
which  the  paper  screen  appears  equally  illuminated  from  both 
sides.    At  this  point  the  oiled  spot  will  either  entirely  disappear 
or  will  at  least  appear  just  alike  when  viewed  from  either  side. 
Measure  the  distance  from  the  single  candle  to  the  screen  and 
also  that  from  the  group  of  candles  to  the  screen.    The  intensi- 
ties of  the  two  sources  are  evidently  in  the  ratio  1  to  4.     What 
is  the  ratio  of  the  distances  ?    What  is  the  ratio  of  the  squares 
of  the  distances  ?     How,  then,  does  the  intensity  of  the  light 
from  a  given  source  vary  with  the  distance  from  that  source? 

II.  Candle  power.    Replace  the  four  candles  by  a  gas  flame 
or  an  electric  lamp,  and  find  by  the  law  just  discovered  to  how 
many  candles  it  is  equivalent,  i.e.  find  its  candle  power. 

1  This  is  an  extra  experiment  inserted  only  for  the  sake  of  schools  which  are 
equipped  with  a  dark  room.  Since  it  is  impossible  to  have  all  of  the  students 
working  upon  it  at  the  same  time,  even  with  a  dark  room,  it  is  a  subject  which, 
when  classes  are  large,  the  authors  prefer  to  treat  from  the  class  room  rather 
than  from  the  laboratory  standpoint. 


APPENDIX  A 


SUGGESTED  TIME  SCHEDULE   FOR  A  ONE-YEAR  COURSE 


CHAP- 
TER 

SUBJECT 

TIME 
ALLOTTED 

EXPERIMENTS 
ACCOMPANYING 

1 

Measurement 

1    week 

1  and  part  of  2 

2 

Force  and  Motion   

2|  weeks 

2to5 

3 

Pressure  in  Liquids      ...... 

2    weeks 

6  and  7 

4 

Pressure  in  Air  

2    weeks 

8  and  9 

5 

Molecular  Motions  

2   weeks 

10  to  12 

6 

Molecular  Forces     

1    week 

13  and  14 

7 

Therinometry  and  Expansion    .     .     . 

1    week 

15 

8 

Work  and  Mechanical  Energy  .     .     . 

2   weeks 

16  to  18 

9 

Work  and  Heat  Energy   

2    weeks 

19  to  21 

10 

Change  of  State 

1    week 

22  and  23 

11 

Transference  of  Heat  . 

^    week 

24 

12 

Magnetism     ... 

^    week 

25 

13 

Static  Electricity     

2   weeks 

26,  27,  and  part  of  28 

14 

Electricity  in  Motion  

2  J-  weeks 

28  to  31 

15 

f  Chemical,    Magnetic,    and    Heating"! 
\     Effects  of  Currents     ) 

1  1  weeks 

32  and  33 

16 

Induced  Currents 

21  weeks 

34  to  37 

17 

Nature  and  Transmission  of  Sound     . 

2    weeks 

38  to  40 

18 

Properties  of  Musical  Sounds    .     .     . 

1  J  weeks 

41  and  42 

19 

Nature  and  Propagation  of  Light   .     . 

2   weeks 

43  to  45 

20 

Image  Formation    

2   weeks 

46  to  48 

21 

Color  Phenomena    

l\  weeks 

48  and  49 

22 

Invisible  Radiation       

1    week 

50 

Total  

3G  weeks 

. 

129 


APPENDIX  B 


RESISTANCES  OF  COPPER  AND  OF  GERMAN  SILVER  WIRE 
BROWN  AND  SHAEP  GAUGE 


PURE  COPPER 

18%  GERMAN  SILVER 

Number 

Diameter  in  Mils 

(nV,in.) 

Ohms  per  1000  ft. 

Ohms  per  1000  ft. 

15 

57.07 

3.314 

59.652 

16 

50.82 

4.179 

76.222 

17 

45.26 

6.269 

94.842 

18 

40.30 

6.645 

119.610 

19 

35.89 

8.617 

155.106 

20 

31.96 

10.566 

11)0.188 

21 

28.46 

13.323 

239.814 

22 

25.35 

16.799 

302.382 

23 

22.57 

21.185 

381.330 

24 

20.10 

26.713 

480.834 

25 

17.90 

33.684 

606.312 

26 

15.94 

42.477 

764.586 

27 

14.20 

63.563 

964.134 

28 

12.64 

67.542 

1215.756 

29 

11.26 

85.170 

1533.060 

30 

10.03 

107.391 

1933.038 

31 

8.93 

135.402 

2437.236 

32 

7.95 

170.765 

3073.770 

33 

7.08 

215.312 

3875.616 

34 

6.30 

271.583 

4888.494 

35 

5.61 

342.443 

6163.974 

36 

5.00 

431.712 

7770.816 

37 

4.45 

544.287 

9797.166 

38 

3.97 

686.511 

12357.198 

39 

3.53 

865.046 

15570.828 

40 

3.14 

1091.865 

19653.570 

130 


APPENDIX   C 

APPARATUS 

This  list  includes  all  of  the  pieces  which  are  desirable  for  the  thoroughly  satisfactory 
onduct  of  the  preceding  course.    The  total  cost  of  a  single  set  can  be  reduced  about  $20  by 
mitting  a  few  pieces  which,  while  desirable,  are  not  at  all  essential.    Some  of  the  more 
xpensive  pieces  do  not  need  duplication  even  for  large  classes,  so  that  the  average  cost  of 

set  is  considerably  less  than  the  total  given  below. 

meter  stick,  p.  1  

$0.25 

1  Boyle's  law  tube,  p.  27      .     . 

$0.30 

brass  disk,  p.  1     

.25' 

1  tripod,    rod,    clamp,    burette 

balance  with  counterpoise,  pp. 

holder,  pp.  27,  37,  47,  48,  110, 

6,.  19  

10.00 

120,  124      

1.75 

1  set  weights  with  holder,  pp.  5, 

3  bottles  125  cc.,  pp.  18,  30  .     . 

.10 

19,  35,  36    

1.60 

3  evaporating  dishes  5  cm.,  p.  30 

.25 

1  Brown  and  Sharp  micrometer 

1  mirror  scale  and  support,  pp. 

caliper  with  ratchet  stop,  p. 

35,  36,  41    

1.25 

9  

5.00 

1  thermometer,  -  20°  C.  to  110°C. 

.50 

2    brass    cylinders    with    glass 

1  spring  and  weight  holder  for 

cover,  pp.  3,  10,  55,  67  ... 

.80* 

Hooke's  law,  p.  35  .     .     .     . 

.35 

8  steel  balls  2  cm.  diameter,  pp. 

1  dew-point  apparatus,  p.  33     . 

1.00 

10  48   74 

.40 

1  steel  rod  *  2  wooden  support 

3  spring  balances,  2000  g.,  pp. 

blocks,  pp.  36,  41,  73,  120,  122 

.75 

11,  13     

1.65 

1  pressure-coefficient-of-air  ap- 

1 parallelogram  law  board,  p. 

paratus,  f>.  37  

1.75 

13      

1.25 

1  tube  for  volume  coefficient  of 

1  glass  tube  110  cm.  by  4  cm., 

air,  p.  39    

.15 

ends  annealed,  rubber  stopper, 

1  steam  generator,  pp.  37,  39,  41, 

pp.  14,  22,  110     

1.75 

55,69     

1.90 

1  manometer  bottle  with  inlet 

1  apparatus  for  expansion  coeffi- 

tube, pinchcock  and  manom- 

cient of  brass,  p.  41  .     .     .     . 

.75 

eters,  p.  18      

1.60 

1  demonstration  balance  (knife- 

1  aluminum  cylinder,  p.  19  .     . 

.40 

edge  and  support),  p.  44   .     . 

.65 

1   constant-weight    hydrometer 

1  inclined  plane  and  sonometer, 

tube,  p   22  .     . 

.40 

pp.  47,  111       

1.55 

1  constant-volume   hydrometer 

1   carriage  for  inclined  plane, 

tube,  p.  23  

.30 

P-  47  

.90 

1  wooden  block  with  sinker,  pp. 

1  pendulum  clamp,  p.  48      .     . 

.35 

24,  25     

.30 

1  boiling-point-of-alcohol  tube  . 

.30 

131 

132 


LABORATORY  PHYSICS 


1   spun-brass  calorimeter,   two 

vessels,  300  cc.  and  1000  cc.,  ^ 

pp.  52,  55,  59,  65,  67,  77    .     .   82.50 
1  tube  for  mechanical  equivalent 

of  h$at,  p.  59 65" 

1  high-grade  compass,  pp.  71,  80, 

83,  88,  90,  92,  94,  98,  100  .  .  1.35*" 
1  small  bottle  acetamide,  p.  63  .  .50 
1  bar  magnet,  pp.  70,  103  .  .  .40 
1  horseshoe  magnet,  pp.  71,  105  .25 
1  electroscope,  pp.  74,  77,  78  .  .50 
1  galvanometer  frame  with  three 

windings,  pp.  80,  88,  90,  92, 

93,97,100 1.60 

1  simple  voltaic  cell  (complete), 

pp.  80,  83,  86,  88,  90,  101       .       .65 
1  pordus  cup  for  Daniell  cell,  pp. 

81,  87,  91,  97,  100 10 

1  D'Arsonval  galvanometer 

(complete),  pp.  86,   96,    103. 

104,  105 2.20 

1  1000-ohm  resistance  coil,  pp. 

87,  90,  101 30 

1  each  of  carbon,  aluminum,  and 

lead  electrodes,  p.  89    ...       .16 


2  lead  electrodes,  p.  101  .     .     .  $0 
1  Wheatstone's  bridge  with  po- 
tentiometer   attachment,   pp. 

81,  92,  94 2.20 

1  commutator,  pp.  83,  86,  104   .       .75 

1  1-ohm  resistance  coil     ...       .40 

2  dry  cells,  pp.  99,  104,  106  .     .       .45 
2  coils  for  induction,  pp.   103, 

104,  105 1.00 

1  electric  bell,  p.  106 30 

2  electric  push  buttons,  p.  106  .       .25 
1  electric  motor,  mounted,  p.  106     1.25 

3  tuning  forks  (256,  384,  512), 

pp.  110.  Ill 3.00 

1  fork-rating  apparatus,  p.  108  .     3.75 

1  glass  plate,  lacquered  black  on 
back,  p.  113 05 

2  prisms,  pp.  116,  116,  125,  126, 

127 2.20 

1  concave  mirror,  p.  118  ...       .45 

1  convex,  mounted  reading  lens, 

pp.  119,  122 45 

2  linen  tester  lenses,  pp.  121, 123      .65 
1  microscope  tube,  p.  124      .     .       .20 

Total 68.00 


INDEX 


Aluminum,  20,  55. 
Amalgamation,  effect  of,  79. 
Ammeter,  97,  101. 
Ampere's  rule,  82. 
Archimedes'  principle,  19. 

Balance,  6  ;  spring,  11. 

Bar  magnets,  70. 

Boiling  point,  of  alcohol,  66  ;  of  water, 

69. 
Boyle's  law,  26. 

Caliper,  vernier,  4  ;  micrometer,  9. 

Calorimeter,  52. 

Candle  power,  128. 

Charge  on  surface,  76. 

Combinations  of  cells,  90,  98. 

Compass,  71. 

Condenser,  electric,  78. 

Conductors,  74. 

Convex  lens,  120. 

Cooling,  by  evaporation,  30 ;  through 

change  of  state,  62. 
Critical  angle,  116. 
Cylinder,  volume  of,  3. 

Daniel  cells,  81. 

Density,  of  steel  spheres,  8 ;  by  loss  of 

weight,  20  ;  of  liquids,  21 ;  of  light 

solids,  24. 
Dew-point,  33. 

Disk  for  determination  of  n,  1. 
Dispersion,  125. 
Dynamo,  105. 


Electric  bells,  106. 
Electrolysis,  99. 
Electrolytes,  89. 
Electro-magnet,  86. 
Electromotive  force,  87. 
Electroplating,  100. 
Electroscope,  74. 
Expansion,  of  air,  37 ;  of  brass,  40. 

Focal  length  of  mirror,  118;  of  lens, 

119. 
Freezing  by  evaporation,  35. 

Galvanometer,  suspended  needle  form, 
80 ;  D'Arsonval  form,  87,  103.  - 

Gasoline,  15. 

Graph,  of  direct  proportion,  16 ;  of  in- 
verse proportion,  29. 

Heat  of  fusion  of  ice,  64. 

Helix,  magnetic  effect  of,  85. 

Hooke's  law,  for  stretching,  35  ;  for 
bending,  36. 

Humidity,  34. 

Hydrometer,  constant  weight,  22 ;  com- 
mercial, 23 ;  constant  volume,  23. 

Hygrometric  table,  34. 

Hyperbola,  30. 

Inclined  plane,  46. 
Index  of  refraction,  114. 
Induction,  magnetic,  73 ;  electrostatic, 
76 ;  electro-magnetic,  102  ;  coil,  104. 


134 


IXDEX 


Law  of  inverse  squares,  128. 
Leclanche",  82. 

Magnetic  fields,  70. 
Magnetism,  molecular  nature  of,  71. 
Magnifying  power,  of  simple  lens,  121 ; 
of  telescope,  123 ;  of  microscope,  124. 
Manometers,  17. 

Mechanical  equivalent  of  heat,  59. 
Microscope,  compound,  123. 
Mirror  scale,  35. 

Mirrors,  plane,  113;  concave,  118. 
Mixtures,  law  of,  52. 
Moments,  principle  of,  44. 
Motor,  106. 

Naphthaline,  64. 
Ohm's  law,  91. 

Parallelogram  of  force,  8. 
Pendulum,  laws  of,  48. 
Per  cent  of  error,  2. 
Phoiometry,  128. 
Polarization  of  a  cell,  80. 
Pressure,  in  liquids,  14 ;  within  a  bot- 
tle, 18. 
Prisms,  128. 
Proportion,  direct,  15 ;  inverse,  29. 

Reflection,  laws  of,  113. 
Resistance,  measurement  of,  93 ;  inter- 
nal resistance  of  cells,  97. 


Resultant,  of   parallel   forces,  11;   of 
concurrent  forces. 

Saturation,  32. 

Solidification  of  acetamide,  62. 

Sonometer,  111. 

Specific  heat,  55. 

Specific  induction  capacity,  79. 

Spectra,  bright-line,  126. 

Speed  of  sound,  107. 

Spring  balance,  11. 

Static  electricity,  74. 

Steel  spheres,  density  of,  8. 

Storage  battery,  100. 

Telescope,  astronomical,  122. 
Temperature  of  white-hot  body,  58. 
Thermometer,  fixed  points  of,  68. 
Total  reflection,  116,  127. 
Tubes  for  Boyle's  law,  27. 

Vernier  caliper,  4. 
Vibrating  strings,  111. 
Vibration  of  a  fork,  rate  of,  111. 
Voltaic  cell,  79. 
Voltmeter,  88,  90,  101. 

Wave  length  produced  by  tuning  fork, 

110. 
Weighing,  method  of  substitution,  6; 

usual  method,  7. 
Wheatstone's  bridge,  94. 


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